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Question 3500: Location of a Coordinate Point

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0005-03500 · q-20260930-r07-coordinate-location-0025

Original question and givens

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.

  • G001 — 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.

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.

Step-by-step derivation

S001 · implies

Before

P=(2,2) in one declared rectangular frame

After

first component=x;second component=y

Conditions: none

In the same coordinate frame,the ordered pair lists horizontal before vertical;do not swap components or infer missing values from a drawing.

Step identifiers and dependencies

Rule: ordered_coordinate_convention · Uses: G001

S002 · implies

Before

x=0:No;y=0:No;signs=(1,1)

After

first quadrant

Conditions: none

Check the origin and axes first,then classify quadrants by signs of two nonzero coordinates.Axis points belong to no quadrant.

Step identifiers and dependencies

Rule: coordinate_location_partition · Uses: G001, S001

Reverse checks

  • S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

quadrant I

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: db035659fe00490b480197d13726600812e5f67404ff712093cc21d700639b9f
  • candidate record SHA-256: c54ff4e5992842d142f16b7bd5467dd97634e35826e36dc895ca40161a35f3d3
  • semantic review receipt SHA-256: 5d74de11610ebc6037a4fc9946d77154d4ed18389f8f0feeb823148b6320c4c2
  • question-first witness SHA-256: 1fba4ab0f13c2cfcc4d9fdebe492c442d43dd45700394a443daa28f333355ed9
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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