{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0001","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fa03f5151298d271607842c28f87673eb591894eaacfd3ea6c025122af859ffe","family_id":"qf-coordinate-location","seed":202609307001,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":-2,\"y\":-2}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(-2,-2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant III","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant III; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0002","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7aa634da5c99d184cd3c7ef59002045d88386389b82b73681303208cb8f46ad6","family_id":"qf-coordinate-location","seed":202609307002,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":-2,\"y\":-1}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(-2,-1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant III","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant III; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0003","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fbe267070cb48306eb396565a739acf803a802b7fbbd5f67e6900917d55756de","family_id":"qf-coordinate-location","seed":202609307003,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":-2,\"y\":0}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(-2,0) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"x-axis","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at x-axis; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0004","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bfec27bdf336e82087bcabe39bf66458e24e3e23e55e7230a1e23c8f800a1628","family_id":"qf-coordinate-location","seed":202609307004,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":-2,\"y\":1}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(-2,1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant II","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant II; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0005","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1080bba91a7fe0d20db88ae27e34f44ca7392a60ce8f2160467fcbf3ca86704f","family_id":"qf-coordinate-location","seed":202609307005,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":-2,\"y\":2}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(-2,2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant II","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant II; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0006","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d5f979a81682d1be29901534baa3908ad61589ce322be7e086534ed9a7fd6b98","family_id":"qf-coordinate-location","seed":202609307006,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":-1,\"y\":-2}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(-1,-2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant III","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant III; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0007","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9a80ef97d7aed83f028bcf2ac99eb45b4804cdcfd0f927902d4ac05260f2a443","family_id":"qf-coordinate-location","seed":202609307007,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":-1,\"y\":-1}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(-1,-1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant III","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant III; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0008","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"71ef9d60ac8c41412d5094d8b07926c27a3e5002d55eef82d43b9334840d80a6","family_id":"qf-coordinate-location","seed":202609307008,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":-1,\"y\":0}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(-1,0) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"x-axis","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at x-axis; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0009","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9830d1e14310767ac5858207c72303e06228dcfa4fc945d7201ef51e7ff93b81","family_id":"qf-coordinate-location","seed":202609307009,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":-1,\"y\":1}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(-1,1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant II","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant II; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0010","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ccf5927820937d878881284ed521abed7cff987c2bda68ee86b7951bc76a5c2d","family_id":"qf-coordinate-location","seed":202609307010,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":-1,\"y\":2}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(-1,2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant II","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant II; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0011","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c01b817c3c4f0ae29a4343d724605fd75345656d3231b268415731b1ac84881b","family_id":"qf-coordinate-location","seed":202609307011,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":0,\"y\":-2}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(0,-2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"y-axis","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at y-axis; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0012","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5bf526b52f8e969edc0ac2b6f2a2812d8e1ad61d789c6566cbea06294dbdc1b7","family_id":"qf-coordinate-location","seed":202609307012,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":0,\"y\":-1}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(0,-1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"y-axis","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at y-axis; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0013","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"70a52c353ecf3cc778fc7b7ab5453a965e37b492bdbfe961e2685dd697c0cd04","family_id":"qf-coordinate-location","seed":202609307013,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":0,\"y\":0}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(0,0) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"origin","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at origin; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0014","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a581c6b2ebb93f710b315d0d772c0ee946cec7abe1ed469eb0f5e01adc006ade","family_id":"qf-coordinate-location","seed":202609307014,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":0,\"y\":1}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(0,1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"y-axis","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at y-axis; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0015","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c8c30ca992c813402ab875cc154f6b03784e04c7e89bf32ce58055203a55945d","family_id":"qf-coordinate-location","seed":202609307015,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":0,\"y\":2}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(0,2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"y-axis","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at y-axis; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0016","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0ab86a340c4d48f08deb740945fdbecb8c1ef29fb0c67a6300edf42c61e37e4a","family_id":"qf-coordinate-location","seed":202609307016,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":1,\"y\":-2}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(1,-2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant IV","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant IV; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0017","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"39f51774a0243b377edb55137bb48598bcdfe634939fb965cc577a745a418864","family_id":"qf-coordinate-location","seed":202609307017,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":1,\"y\":-1}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(1,-1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant IV","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant IV; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0018","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"679099d14e3c1f551a51dff7cdfdb5204f910052db36942bbfb8b82dcf020352","family_id":"qf-coordinate-location","seed":202609307018,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":1,\"y\":0}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(1,0) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"x-axis","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at x-axis; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0019","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a83384961e85aab057cb68084d186b0fba4db77e8f0f42de848555da06cfef13","family_id":"qf-coordinate-location","seed":202609307019,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":1,\"y\":1}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(1,1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant I","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant I; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0020","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"41091e227b22ab4ad5676a3db0fea0ecf87a63142df9c6a7eaf65e00e60c4c32","family_id":"qf-coordinate-location","seed":202609307020,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":1,\"y\":2}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(1,2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant I","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant I; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0021","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"76fe78188184c03904b34f699569ec0cc149e4b00d68d2151eb4e995dc6c5847","family_id":"qf-coordinate-location","seed":202609307021,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":2,\"y\":-2}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(2,-2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant IV","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant IV; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0022","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e9f630c7fe9e593e4ed8e1cb85054e3a6179761a42c73fdb257fd0ce0b914edf","family_id":"qf-coordinate-location","seed":202609307022,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":2,\"y\":-1}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(2,-1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant IV","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant IV; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0023","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9a8bdb28d85cf0eb08a244dde80fbcb562bb72d3565c7255e70cb926ef2c96c5","family_id":"qf-coordinate-location","seed":202609307023,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":2,\"y\":0}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(2,0) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"x-axis","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at x-axis; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0024","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ba1c3cdac42a2e7ee7d344465e1ede07e66e4af0f9af862ddd08b1b903fed35","family_id":"qf-coordinate-location","seed":202609307024,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":2,\"y\":1}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(2,1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant I","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant I; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-location-0025","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"db035659fe00490b480197d13726600812e5f67404ff712093cc21d700639b9f","family_id":"qf-coordinate-location","seed":202609307025,"semantic_template":"qf-coordinate-location/{\"operation\":\"location\",\"x\":2,\"y\":2}"},"fields":{"title":"Location of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, classify P=(2,2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.","answer":{"kind":"short_text","value":"quadrant I","explanation":"Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant I; the origin lies on both axes."},"skills":["coordinate signs","axes and quadrants"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0001","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c018ac1d22cd8482577322654ddb9d734b35bbca13f10934b35066e26f3fa16d","family_id":"qf-coordinate-axis-membership","seed":202609307101,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"x\",\"operation\":\"axis_membership\",\"x\":-2,\"y\":-2}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(-2,-2) on the x-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The x-axis condition is y=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0002","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"38829d495e96bfea692bea53b1f7ca87a654bf1c861813996147ca912201ee7b","family_id":"qf-coordinate-axis-membership","seed":202609307102,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"y\",\"operation\":\"axis_membership\",\"x\":-2,\"y\":-1}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(-2,-1) on the y-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The y-axis condition is x=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0003","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"989bbc5ec32441b056df74874aa318afbbf451f72c04cafb3e2b4fa17849a866","family_id":"qf-coordinate-axis-membership","seed":202609307103,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"x\",\"operation\":\"axis_membership\",\"x\":-2,\"y\":0}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(-2,0) on the x-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"Yes","explanation":"The x-axis condition is y=0. Componentwise checking gives Yes."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0004","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d84dc25eac7e9c8c2a8669447792c4ee245bfdbb092451439becdb7f0e348e9e","family_id":"qf-coordinate-axis-membership","seed":202609307104,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"y\",\"operation\":\"axis_membership\",\"x\":-2,\"y\":1}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(-2,1) on the y-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The y-axis condition is x=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0005","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bb572e862790fb5da5583bd2e26938d9b9f4017a868727f74b4c083af616caca","family_id":"qf-coordinate-axis-membership","seed":202609307105,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"x\",\"operation\":\"axis_membership\",\"x\":-2,\"y\":2}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(-2,2) on the x-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The x-axis condition is y=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0006","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a1d1b8305f10ae7fb678b54df998c31d32f261b2861e731444aac51a2efb920d","family_id":"qf-coordinate-axis-membership","seed":202609307106,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"y\",\"operation\":\"axis_membership\",\"x\":-1,\"y\":-2}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(-1,-2) on the y-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The y-axis condition is x=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0007","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"059d469435f515cb996d8aa2fbfbfb27bd9336eabe62efc4f6711c87097e4b72","family_id":"qf-coordinate-axis-membership","seed":202609307107,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"x\",\"operation\":\"axis_membership\",\"x\":-1,\"y\":-1}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(-1,-1) on the x-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The x-axis condition is y=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0008","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"838ce285d4a4cd142a266787a94c64e0757a86dd3a1c39580b3dfba0eccf54fb","family_id":"qf-coordinate-axis-membership","seed":202609307108,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"y\",\"operation\":\"axis_membership\",\"x\":-1,\"y\":0}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(-1,0) on the y-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The y-axis condition is x=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0009","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aadd08b4e8a58a62f14347ca0fd72adc8e666bd12dce892722f2774f452d02cf","family_id":"qf-coordinate-axis-membership","seed":202609307109,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"x\",\"operation\":\"axis_membership\",\"x\":-1,\"y\":1}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(-1,1) on the x-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The x-axis condition is y=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0010","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dd9bef15cabe5726a30e26a7928bfef7349473a7c7a9f2c4f91b17fa8bc1e77e","family_id":"qf-coordinate-axis-membership","seed":202609307110,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"y\",\"operation\":\"axis_membership\",\"x\":-1,\"y\":2}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(-1,2) on the y-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The y-axis condition is x=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0011","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3837399918223e05b592a13b53e3a092840070e6cffc60cd77e0ae8c46abeb3f","family_id":"qf-coordinate-axis-membership","seed":202609307111,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"x\",\"operation\":\"axis_membership\",\"x\":0,\"y\":-2}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(0,-2) on the x-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The x-axis condition is y=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0012","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"77354c3d7f2b89bdb6d54f55ec44275d5fa6768339145d52f56c1c1ea9e9e2d6","family_id":"qf-coordinate-axis-membership","seed":202609307112,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"y\",\"operation\":\"axis_membership\",\"x\":0,\"y\":-1}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(0,-1) on the y-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"Yes","explanation":"The y-axis condition is x=0. Componentwise checking gives Yes."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0013","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c0409293fe931544e2684cd472cca52c5422aaf815346b08fc9c0893ea95dde4","family_id":"qf-coordinate-axis-membership","seed":202609307113,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"x\",\"operation\":\"axis_membership\",\"x\":0,\"y\":0}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(0,0) on the x-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"Yes","explanation":"The x-axis condition is y=0. Componentwise checking gives Yes."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0014","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0b433ded80a4252e717bd939938c7d3bfa91454b01bf08d53a465f767453c3c8","family_id":"qf-coordinate-axis-membership","seed":202609307114,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"y\",\"operation\":\"axis_membership\",\"x\":0,\"y\":1}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(0,1) on the y-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"Yes","explanation":"The y-axis condition is x=0. Componentwise checking gives Yes."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0015","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cd11ba1546a4c2e28933a697c401713d98e1e4fa02985b12b80c9111db817655","family_id":"qf-coordinate-axis-membership","seed":202609307115,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"x\",\"operation\":\"axis_membership\",\"x\":0,\"y\":2}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(0,2) on the x-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The x-axis condition is y=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0016","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"175a19a2175818c4520c64376d2f6a8dd1d08abd0d2b946008b9fd1ac336eacc","family_id":"qf-coordinate-axis-membership","seed":202609307116,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"y\",\"operation\":\"axis_membership\",\"x\":1,\"y\":-2}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(1,-2) on the y-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The y-axis condition is x=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0017","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"96e6eccd01182787f5564468b7dfdd438f12d8ad15ebf1e872c521ecd11d4b12","family_id":"qf-coordinate-axis-membership","seed":202609307117,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"x\",\"operation\":\"axis_membership\",\"x\":1,\"y\":-1}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(1,-1) on the x-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The x-axis condition is y=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0018","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7f1327791bfeb9c7eda8a8f2a55a561187c4afdf6d5e14feb7d78b85d1dd3e2a","family_id":"qf-coordinate-axis-membership","seed":202609307118,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"y\",\"operation\":\"axis_membership\",\"x\":1,\"y\":0}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(1,0) on the y-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The y-axis condition is x=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0019","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"126c7ab9a7ee4ef130d4666030a6c2c615246417ddfa80031fc56e2ceb222c85","family_id":"qf-coordinate-axis-membership","seed":202609307119,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"x\",\"operation\":\"axis_membership\",\"x\":1,\"y\":1}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(1,1) on the x-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The x-axis condition is y=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0020","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0ef9257ada2dc3d5c59ca9c8e5dd4866d60c54b3b4f4eba28e6bea306bcd2c8e","family_id":"qf-coordinate-axis-membership","seed":202609307120,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"y\",\"operation\":\"axis_membership\",\"x\":1,\"y\":2}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(1,2) on the y-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The y-axis condition is x=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0021","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"785b8f4f9b9c6aa8a2e6b217e8c79b4124644f462110c21717fbcbade09267f9","family_id":"qf-coordinate-axis-membership","seed":202609307121,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"x\",\"operation\":\"axis_membership\",\"x\":2,\"y\":-2}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(2,-2) on the x-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The x-axis condition is y=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0022","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"93855c5af62a1113f4c00305b79d4878b098e8f0fdf49bb419340250a73fd575","family_id":"qf-coordinate-axis-membership","seed":202609307122,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"y\",\"operation\":\"axis_membership\",\"x\":2,\"y\":-1}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(2,-1) on the y-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The y-axis condition is x=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0023","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"39a53ce62792e2adb65004691ce79ac151d187d3893a3f70fa1d550c15ae45df","family_id":"qf-coordinate-axis-membership","seed":202609307123,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"x\",\"operation\":\"axis_membership\",\"x\":2,\"y\":0}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(2,0) on the x-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"Yes","explanation":"The x-axis condition is y=0. Componentwise checking gives Yes."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0024","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6cd29a6cf360dce00c5fde5bd8b5bf6036dbc04e466cb50058e15ccc9affb5df","family_id":"qf-coordinate-axis-membership","seed":202609307124,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"y\",\"operation\":\"axis_membership\",\"x\":2,\"y\":1}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(2,1) on the y-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The y-axis condition is x=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-axis-membership-0025","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"478b945e1d70ca2b27e56e77d0283dfa73b8a1335069ec7d62cd4b5a27d7c8b9","family_id":"qf-coordinate-axis-membership","seed":202609307125,"semantic_template":"qf-coordinate-axis-membership/{\"axis\":\"x\",\"operation\":\"axis_membership\",\"x\":2,\"y\":2}"},"fields":{"title":"Axis Membership of a Coordinate Point","stem":"In one explicit Cartesian coordinate system, is P=(2,2) on the x-axis? Answer Yes or No; the origin belongs to both axes.","answer":{"kind":"short_text","value":"No","explanation":"The x-axis condition is y=0. Componentwise checking gives No."},"skills":["zero coordinates","origin boundary"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0001","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a5413ee0130a0bbb8026a0e7c0cd84d5b586db3efb9536ac49c3485e0b8cc624","family_id":"qf-coordinate-component","seed":202609307201,"semantic_template":"qf-coordinate-component/{\"component\":\"x\",\"operation\":\"component\",\"x\":-2,\"y\":-2}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the x-coordinate of P=(-2,-2)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"-2","explanation":"The first component is -2, so the x-coordinate is -2."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0002","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"03c4a65ac901d8b08a77f9fd07d6f35a17df4af5d05ad62389b103500b0d42d6","family_id":"qf-coordinate-component","seed":202609307202,"semantic_template":"qf-coordinate-component/{\"component\":\"y\",\"operation\":\"component\",\"x\":-2,\"y\":-1}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the y-coordinate of P=(-2,-1)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"-1","explanation":"The second component is -1, so the y-coordinate is -1."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0003","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f6e83d7c8b629230936b9f8611750216da6d398a26e8e7dfaca7e22664c3b18a","family_id":"qf-coordinate-component","seed":202609307203,"semantic_template":"qf-coordinate-component/{\"component\":\"x\",\"operation\":\"component\",\"x\":-2,\"y\":0}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the x-coordinate of P=(-2,0)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"-2","explanation":"The first component is -2, so the x-coordinate is -2."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0004","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3df4a80a8ece2e26f89e816aecb99aeb94c990db58b1dc85fe1ea98f99a15d83","family_id":"qf-coordinate-component","seed":202609307204,"semantic_template":"qf-coordinate-component/{\"component\":\"y\",\"operation\":\"component\",\"x\":-2,\"y\":1}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the y-coordinate of P=(-2,1)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"1","explanation":"The second component is 1, so the y-coordinate is 1."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0005","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e30e8f39f54fc994a8da8981177066e750db3634bdbc106095c9729f3f701580","family_id":"qf-coordinate-component","seed":202609307205,"semantic_template":"qf-coordinate-component/{\"component\":\"x\",\"operation\":\"component\",\"x\":-2,\"y\":2}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the x-coordinate of P=(-2,2)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"-2","explanation":"The first component is -2, so the x-coordinate is -2."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0006","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a36cb5f59388e975503651d86728cddf9bd76d4649b83f7f38a9a4bea5fcbe2e","family_id":"qf-coordinate-component","seed":202609307206,"semantic_template":"qf-coordinate-component/{\"component\":\"y\",\"operation\":\"component\",\"x\":-1,\"y\":-2}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the y-coordinate of P=(-1,-2)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"-2","explanation":"The second component is -2, so the y-coordinate is -2."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0007","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c3186b616e5e8b4797f48c3346fc141142ad7c645bc8680d0527cd9030700133","family_id":"qf-coordinate-component","seed":202609307207,"semantic_template":"qf-coordinate-component/{\"component\":\"x\",\"operation\":\"component\",\"x\":-1,\"y\":-1}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the x-coordinate of P=(-1,-1)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"-1","explanation":"The first component is -1, so the x-coordinate is -1."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0008","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"27f5fea4e4445c78325b134bd005cd0855592f6a3058bfb179dac1c2d733f311","family_id":"qf-coordinate-component","seed":202609307208,"semantic_template":"qf-coordinate-component/{\"component\":\"y\",\"operation\":\"component\",\"x\":-1,\"y\":0}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the y-coordinate of P=(-1,0)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"0","explanation":"The second component is 0, so the y-coordinate is 0."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0009","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"526ec4deb2b7d09351a4e714eae14a7558bc59d0d7e0c5740f20fcd9fe32bfea","family_id":"qf-coordinate-component","seed":202609307209,"semantic_template":"qf-coordinate-component/{\"component\":\"x\",\"operation\":\"component\",\"x\":-1,\"y\":1}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the x-coordinate of P=(-1,1)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"-1","explanation":"The first component is -1, so the x-coordinate is -1."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0010","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fea08554784c3b4cc3a567db58f6790d28a2c25e455823e88e5ee1bb6ac3d70c","family_id":"qf-coordinate-component","seed":202609307210,"semantic_template":"qf-coordinate-component/{\"component\":\"y\",\"operation\":\"component\",\"x\":-1,\"y\":2}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the y-coordinate of P=(-1,2)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"2","explanation":"The second component is 2, so the y-coordinate is 2."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0011","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ba421ccd38eeef0a5806e47967487ba62ecb6ca8a7878b58faf6470774bbbaf","family_id":"qf-coordinate-component","seed":202609307211,"semantic_template":"qf-coordinate-component/{\"component\":\"x\",\"operation\":\"component\",\"x\":0,\"y\":-2}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the x-coordinate of P=(0,-2)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"0","explanation":"The first component is 0, so the x-coordinate is 0."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0012","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"68395b186fbd8182038ae636648b55e10640a662270a66dd94bd0af5fab14370","family_id":"qf-coordinate-component","seed":202609307212,"semantic_template":"qf-coordinate-component/{\"component\":\"y\",\"operation\":\"component\",\"x\":0,\"y\":-1}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the y-coordinate of P=(0,-1)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"-1","explanation":"The second component is -1, so the y-coordinate is -1."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0013","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"514daaa5042c3cb1a7067211f98b6f2658fae6c82ab009bda30613fac823b9e4","family_id":"qf-coordinate-component","seed":202609307213,"semantic_template":"qf-coordinate-component/{\"component\":\"x\",\"operation\":\"component\",\"x\":0,\"y\":0}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the x-coordinate of P=(0,0)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"0","explanation":"The first component is 0, so the x-coordinate is 0."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0014","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3675fdde8a81ca4256b96791b23347f7c262146db4b75b09fe2c24d3307e45c8","family_id":"qf-coordinate-component","seed":202609307214,"semantic_template":"qf-coordinate-component/{\"component\":\"y\",\"operation\":\"component\",\"x\":0,\"y\":1}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the y-coordinate of P=(0,1)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"1","explanation":"The second component is 1, so the y-coordinate is 1."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0015","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2fbaed4904f460a146502d63548d30fb3785afe5a9d8f45c3173646c239cb545","family_id":"qf-coordinate-component","seed":202609307215,"semantic_template":"qf-coordinate-component/{\"component\":\"x\",\"operation\":\"component\",\"x\":0,\"y\":2}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the x-coordinate of P=(0,2)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"0","explanation":"The first component is 0, so the x-coordinate is 0."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0016","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9bcddde91314a60f59481b4ce3037b1e6e36b4e7a7a5538788ec9fa5f3b5b8f0","family_id":"qf-coordinate-component","seed":202609307216,"semantic_template":"qf-coordinate-component/{\"component\":\"y\",\"operation\":\"component\",\"x\":1,\"y\":-2}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the y-coordinate of P=(1,-2)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"-2","explanation":"The second component is -2, so the y-coordinate is -2."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0017","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7f980dfc69aca4e0348092b2da2c8c71058a5624ccf20cc157af0b46cd095b12","family_id":"qf-coordinate-component","seed":202609307217,"semantic_template":"qf-coordinate-component/{\"component\":\"x\",\"operation\":\"component\",\"x\":1,\"y\":-1}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the x-coordinate of P=(1,-1)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"1","explanation":"The first component is 1, so the x-coordinate is 1."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0018","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c130e9e7e55c77d04e6c25eb460a364abd657c04742ed463dacfb4e1a716cef","family_id":"qf-coordinate-component","seed":202609307218,"semantic_template":"qf-coordinate-component/{\"component\":\"y\",\"operation\":\"component\",\"x\":1,\"y\":0}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the y-coordinate of P=(1,0)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"0","explanation":"The second component is 0, so the y-coordinate is 0."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0019","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0cfedd9c32c6f6f88b700b2df75799438f517cc67ed9a6118bc6ee9326b97f53","family_id":"qf-coordinate-component","seed":202609307219,"semantic_template":"qf-coordinate-component/{\"component\":\"x\",\"operation\":\"component\",\"x\":1,\"y\":1}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the x-coordinate of P=(1,1)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"1","explanation":"The first component is 1, so the x-coordinate is 1."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0020","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"77e77d933fdf64fc9b97d5c0cf0adee1a125786e06df880b7e8ed282a46950ec","family_id":"qf-coordinate-component","seed":202609307220,"semantic_template":"qf-coordinate-component/{\"component\":\"y\",\"operation\":\"component\",\"x\":1,\"y\":2}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the y-coordinate of P=(1,2)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"2","explanation":"The second component is 2, so the y-coordinate is 2."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0021","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e481601a15a52af7cdec604b03c90054c05990e2881f2ccdfb07e80624b5f33c","family_id":"qf-coordinate-component","seed":202609307221,"semantic_template":"qf-coordinate-component/{\"component\":\"x\",\"operation\":\"component\",\"x\":2,\"y\":-2}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the x-coordinate of P=(2,-2)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"2","explanation":"The first component is 2, so the x-coordinate is 2."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0022","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7e986d8a377d2cfa608548dbae2fd9bc080d465bd40678872897ceea9a8ccb88","family_id":"qf-coordinate-component","seed":202609307222,"semantic_template":"qf-coordinate-component/{\"component\":\"y\",\"operation\":\"component\",\"x\":2,\"y\":-1}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the y-coordinate of P=(2,-1)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"-1","explanation":"The second component is -1, so the y-coordinate is -1."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0023","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"045cf79f3f9400e8894b6196bf5f085fe7865a0ebda386af2d42c33954be2f12","family_id":"qf-coordinate-component","seed":202609307223,"semantic_template":"qf-coordinate-component/{\"component\":\"x\",\"operation\":\"component\",\"x\":2,\"y\":0}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the x-coordinate of P=(2,0)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"2","explanation":"The first component is 2, so the x-coordinate is 2."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0024","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"39aebefa4b8efbf7c342adc70919b00e162fd08c2e2f9644d9d8a864c51e82b8","family_id":"qf-coordinate-component","seed":202609307224,"semantic_template":"qf-coordinate-component/{\"component\":\"y\",\"operation\":\"component\",\"x\":2,\"y\":1}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the y-coordinate of P=(2,1)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"1","explanation":"The second component is 1, so the y-coordinate is 1."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-component-0025","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e55246a1503f26b21127085d9494a67c10828db2601194bb72e704a4536df9fc","family_id":"qf-coordinate-component","seed":202609307225,"semantic_template":"qf-coordinate-component/{\"component\":\"x\",\"operation\":\"component\",\"x\":2,\"y\":2}"},"fields":{"title":"Component of an Ordered Coordinate Pair","stem":"In one explicit Cartesian coordinate system, what is the x-coordinate of P=(2,2)? Read the ordered pair as (x,y).","answer":{"kind":"short_text","value":"2","explanation":"The first component is 2, so the x-coordinate is 2."},"skills":["ordered pairs","coordinate roles"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0001","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2835ce11297884e35e12419bcd4698c4cddce957c04fb1b4fd3861abb6857296","family_id":"qf-coordinate-point-equality","seed":202609307301,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":-2,\"v\":-2,\"x\":-2,\"y\":-2}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(-2,-2) and Q=(-2,-2) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"Yes","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives Yes."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0002","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"37651b9e8e653766c5156ee5c9c2d423b7a5a20232fcdf026539a7c16aafd05c","family_id":"qf-coordinate-point-equality","seed":202609307302,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":-1,\"v\":-1,\"x\":-2,\"y\":-1}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(-2,-1) and Q=(-1,-1) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"No","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives No."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0003","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c420a8f3ad47215290fbb6616cd98bd806366580e83922049ae4f014c2659468","family_id":"qf-coordinate-point-equality","seed":202609307303,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":-2,\"v\":0,\"x\":-2,\"y\":0}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(-2,0) and Q=(-2,0) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"Yes","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives Yes."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0004","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3848c94f8d082746751c09df6cd64a437e5c1352d8563832cc1b967728d5c629","family_id":"qf-coordinate-point-equality","seed":202609307304,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":-2,\"v\":2,\"x\":-2,\"y\":1}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(-2,1) and Q=(-2,2) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"No","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives No."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0005","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bfea5eecc745079558988554406270e8126b927714be4478a9ae6c82665304bf","family_id":"qf-coordinate-point-equality","seed":202609307305,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":-2,\"v\":2,\"x\":-2,\"y\":2}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(-2,2) and Q=(-2,2) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"Yes","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives Yes."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0006","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"00f4df00d4a68bd9492cf500dac222674179db63e93011c581a000cb810573a4","family_id":"qf-coordinate-point-equality","seed":202609307306,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":0,\"v\":-2,\"x\":-1,\"y\":-2}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(-1,-2) and Q=(0,-2) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"No","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives No."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0007","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8643e0ca7392f20288aba99ef85f35da1e3008608bb70634068f3b8d877eaa61","family_id":"qf-coordinate-point-equality","seed":202609307307,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":-1,\"v\":-1,\"x\":-1,\"y\":-1}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(-1,-1) and Q=(-1,-1) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"Yes","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives Yes."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0008","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e196d2538d129bf7fd4ee3010aa80a7543b001235c38e1d19a45f5117e767e6b","family_id":"qf-coordinate-point-equality","seed":202609307308,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":0,\"v\":0,\"x\":-1,\"y\":0}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(-1,0) and Q=(0,0) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"No","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives No."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0009","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1ee39cfc3c5dedd25ef65b7d72b5da540d9e6fb00480f6134fabe89e8eaf50f8","family_id":"qf-coordinate-point-equality","seed":202609307309,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":-1,\"v\":1,\"x\":-1,\"y\":1}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(-1,1) and Q=(-1,1) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"Yes","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives Yes."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0010","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"89ff3705b1a5bf956d0faf064cb44833aae8cb6781de52c6b207a0cf2c5805e5","family_id":"qf-coordinate-point-equality","seed":202609307310,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":-1,\"v\":3,\"x\":-1,\"y\":2}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(-1,2) and Q=(-1,3) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"No","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives No."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0011","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"63814f4ece7f2d0fd9b2fea7a8612a78a27deb1e93ee991f79630fad58f65072","family_id":"qf-coordinate-point-equality","seed":202609307311,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":0,\"v\":-2,\"x\":0,\"y\":-2}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(0,-2) and Q=(0,-2) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"Yes","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives Yes."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0012","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e84b2b44f3e48b11f969bec35d1c5e4f30e6538080ad90c3847da60fb529c320","family_id":"qf-coordinate-point-equality","seed":202609307312,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":1,\"v\":-1,\"x\":0,\"y\":-1}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(0,-1) and Q=(1,-1) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"No","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives No."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0013","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ed2df10db00d58983f84d152afdda732283cb3b917989bdd6803d60c1c6f2ea8","family_id":"qf-coordinate-point-equality","seed":202609307313,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":0,\"v\":0,\"x\":0,\"y\":0}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(0,0) and Q=(0,0) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"Yes","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives Yes."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0014","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"211368946659e4046a3a74c721c112befdeba4af71cde5e069f8abe4566973e0","family_id":"qf-coordinate-point-equality","seed":202609307314,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":1,\"v\":1,\"x\":0,\"y\":1}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(0,1) and Q=(1,1) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"No","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives No."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0015","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ae1a7ba4ceeddf287a6578b3931ee6b5b6d2a84c5d418860dc194b08b839b65f","family_id":"qf-coordinate-point-equality","seed":202609307315,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":0,\"v\":2,\"x\":0,\"y\":2}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(0,2) and Q=(0,2) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"Yes","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives Yes."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0016","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5f78f5879dccf7cf5561e617c74ab1fc815556e066afaa64bfad52f70cce73f0","family_id":"qf-coordinate-point-equality","seed":202609307316,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":1,\"v\":-1,\"x\":1,\"y\":-2}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(1,-2) and Q=(1,-1) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"No","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives No."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0017","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aee43fc9abdefac7104985293a7029b00c0057d96404c8f4f2c2eaee6cdb4d8e","family_id":"qf-coordinate-point-equality","seed":202609307317,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":1,\"v\":-1,\"x\":1,\"y\":-1}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(1,-1) and Q=(1,-1) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"Yes","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives Yes."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0018","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"25337faa9707ceba6655ee1c0f0cd90778c331948e9ac468a52b73952ad26db3","family_id":"qf-coordinate-point-equality","seed":202609307318,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":2,\"v\":0,\"x\":1,\"y\":0}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(1,0) and Q=(2,0) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"No","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives No."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0019","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2d0da6458c0c983d2aee4b4257bc66fed40c64f7c09b61a3b2748e26ebd21c42","family_id":"qf-coordinate-point-equality","seed":202609307319,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":1,\"v\":1,\"x\":1,\"y\":1}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(1,1) and Q=(1,1) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"Yes","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives Yes."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0020","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6af7da42de414c3b4df104e371e05e1b208be95a79e694dd106449613bcd415c","family_id":"qf-coordinate-point-equality","seed":202609307320,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":2,\"v\":2,\"x\":1,\"y\":2}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(1,2) and Q=(2,2) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"No","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives No."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0021","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6bee90329de9fcf63a675a729c803d447a7d6356a4bf424142cbc57a2522d061","family_id":"qf-coordinate-point-equality","seed":202609307321,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":2,\"v\":-2,\"x\":2,\"y\":-2}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(2,-2) and Q=(2,-2) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"Yes","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives Yes."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0022","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f5d84e867998a50e8d190d040ef860ccf2676e5ecac0a194a883f59350ed9ee7","family_id":"qf-coordinate-point-equality","seed":202609307322,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":2,\"v\":0,\"x\":2,\"y\":-1}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(2,-1) and Q=(2,0) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"No","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives No."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0023","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0936c4539e0aadc283af0c9a8fcc3f2b81b15d386a194c7fb021d9f889a37793","family_id":"qf-coordinate-point-equality","seed":202609307323,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":2,\"v\":0,\"x\":2,\"y\":0}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(2,0) and Q=(2,0) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"Yes","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives Yes."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0024","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"94e40e42f78ea460055a84b6ea51af50c82d0cf804e4ed22fc42bf40bd98cb44","family_id":"qf-coordinate-point-equality","seed":202609307324,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":3,\"v\":1,\"x\":2,\"y\":1}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(2,1) and Q=(3,1) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"No","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives No."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r07-coordinate-point-equality-0025","batch_id":"batch-20260930-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2c3511e4406581fb312640b5f296b02c83a5bad4b5a0e5f8fec08f8fb4d0388f","family_id":"qf-coordinate-point-equality","seed":202609307325,"semantic_template":"qf-coordinate-point-equality/{\"operation\":\"point_equality\",\"u\":2,\"v\":2,\"x\":2,\"y\":2}"},"fields":{"title":"Equality of Points in One Coordinate System","stem":"In the same explicit Cartesian coordinate system, are P=(2,2) and Q=(2,2) the same point? Compare corresponding coordinates.","answer":{"kind":"short_text","value":"Yes","explanation":"Point equality requires equality of both corresponding components. The componentwise comparison gives Yes."},"skills":["componentwise equality","shared coordinate system"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}