# Question 30756: Four Ordered Coordinate Columns, Axes, and Locations [Return to catalogue page 154](https://ocme.evemisslab.com/en/questions/page/154/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261011-advance-20261015-r07-coordinate-plane-foundations/#q-20261011-advance-20261015-r07-coordinate-plane-0006) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0060-30756 · q-20261011-advance-20261015-r07-coordinate-plane-0006 ## Original question and givens Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[-7, 1], [1, 0], [0, 1], [-1, -5]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications). - G001 — Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[-7, 1], [1, 0], [0, 1], [-1, -5]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications). ## Definition and scope Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate. - [mko-coordinate-plane](https://ocme.evemisslab.com/en/mko/mko-coordinate-plane/) ## Step-by-step derivation S001 · impliesBefore source roles = [qf-density15-coordinate-four-point-axis-masks, density15_coordinate_four_point_axis_masks, finite_ordered_coordinate_protocol] After derived = [[x_column, y_column, x_axis_mask, y_axis_mask, locations]] Conditions: none density14/15 use FULL-prefix underscores;density17 uses LOCAL hyphens.The coordinate and circle frames differ.Retain THIS family ordered answer roles/types and all original bilingual JSON/status. Step identifiers and dependenciesRule: R60_EXACT_perbank_operation_domain_FRAME_and_output_roles · Uses: G001 S002 · impliesBefore source roles = [0, -7, 1] After derived = [No, No, II] Conditions: none Check zero coordinates BEFORE quadrants.The origin lies on BOTH axes and in NO quadrant;axis points are not quadrant points.Keep all four positions and separate x/y columns without diagram guesses. Step identifiers and dependenciesRule: Coordinate_EACH_original_point_axes_BEFORE_quadrants · Uses: G001, S001 S003 · impliesBefore source roles = [1, 1, 0] After derived = [Yes, No, x axis] Conditions: none Check zero coordinates BEFORE quadrants.The origin lies on BOTH axes and in NO quadrant;axis points are not quadrant points.Keep all four positions and separate x/y columns without diagram guesses. Step identifiers and dependenciesRule: Coordinate_EACH_original_point_axes_BEFORE_quadrants · Uses: G001, S002 S004 · impliesBefore source roles = [2, 0, 1] After derived = [No, Yes, y axis] Conditions: none Check zero coordinates BEFORE quadrants.The origin lies on BOTH axes and in NO quadrant;axis points are not quadrant points.Keep all four positions and separate x/y columns without diagram guesses. Step identifiers and dependenciesRule: Coordinate_EACH_original_point_axes_BEFORE_quadrants · Uses: G001, S003 S005 · impliesBefore source roles = [3, -1, -5] After derived = [No, No, III] Conditions: none Check zero coordinates BEFORE quadrants.The origin lies on BOTH axes and in NO quadrant;axis points are not quadrant points.Keep all four positions and separate x/y columns without diagram guesses. Step identifiers and dependenciesRule: Coordinate_EACH_original_point_axes_BEFORE_quadrants · Uses: G001, S004 ## Reverse checks - S005 · premise_and_result_audit — Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate. - S004 · premise_and_result_audit — Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate. - S003 · premise_and_result_audit — Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate. - S002 · premise_and_result_audit — Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate. - S001 · premise_and_result_audit — Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate. ## Result ([-7, 1, 0, -1], [1, 0, 1, -5], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III]) The full substitutions and premise checks give the original answer; source identity,format and status are unchanged. ## This question review and source binding Review date: 2026-10-26 Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof. Source hashes and review receipts - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: b311b8737ea21e99c40ff6e418c626bd2988a6de73d5b7ed9a76bdd33b5adfa1 - candidate record SHA-256: 445597556793d60ebc9f0f54a0c7bc09fe9e4ce7eb0aed781cb270f798bd6bca - semantic review receipt SHA-256: d6b5a409bf933281a46617cd715d8016fd5ca3d6fb76f77d179ac2ecd9d608bf - question-first witness SHA-256: f80ecf598c6893a580af018e1a82849b33ee6887efb48a6a1d69569aa17f12e4 - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261011-advance-20261015-r07-coordinate-plane-0006.json)