# Question 3446: Axis Membership of a Coordinate Point

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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.

R0005-03446 · q-20260930-r07-coordinate-axis-membership-0021



## Original question and givens

In one explicit Cartesian coordinate system, is P=(2,-2) on the x-axis? Answer Yes or No; the origin belongs to both axes.


- G001 — In one explicit Cartesian coordinate system, is P=(2,-2) on the x-axis? Answer Yes or No; the origin belongs to both axes.





## 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

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 dependenciesRule: ordered_coordinate_convention · Uses: G001





S002 · impliesBefore

x=2;y=-2;requested x-axis

After

No

Conditions: none

The x-axis requires y=0 and the y-axis requires x=0.The origin belongs to both axes;the other component need not be nonzero.

Step identifiers and dependenciesRule: axis_zero_coordinate_test · 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

No

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: 785b8f4f9b9c6aa8a2e6b217e8c79b4124644f462110c21717fbcbade09267f9
- candidate record SHA-256: 594eada781a0b57d170f402b4e580c4316087b9393d637b5eb15bfe9d2159fae
- semantic review receipt SHA-256: 5d74de11610ebc6037a4fc9946d77154d4ed18389f8f0feeb823148b6320c4c2
- question-first witness SHA-256: 1fba4ab0f13c2cfcc4d9fdebe492c442d43dd45700394a443daa28f333355ed9
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20260930-r07-coordinate-axis-membership-0021.json)