# Question 29910: Equality of Points in One Coordinate System

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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.

R0058-29910 · q-20260930-r07-coordinate-point-equality-0010



## Original question and givens

In the same explicit Cartesian coordinate system, are P=(-1,2) and Q=(-1,3) the same point? Compare corresponding coordinates.


- G001 — In the same explicit Cartesian coordinate system, are P=(-1,2) and Q=(-1,3) the same point? Compare corresponding coordinates.





## 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-coordinate-point-equality, point_equality]

After

derived = [[ordered_point_equality_yes_no]]

Conditions: none

Follow THIS bank exact keys,domain/frame,operation and answer role.STR22/App20 tuples differ from legacy scalars;retain or omit/1 by the ORIGINAL contract,not a generic visual convention.

Step identifiers and dependenciesRule: R58_EXACT_source_interface_and_answer_ROLE · Uses: G001





S002 · calculationBefore

Coordinate ORIGINAL first component difference x minus u := sub(-1, -1)

After

Coordinate ORIGINAL first component difference x minus u = 0

Conditions: none

Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S001





S003 · calculationBefore

Coordinate ORIGINAL second component difference y minus v := sub(2, 3)

After

Coordinate ORIGINAL second component difference y minus v = -1

Conditions: none

Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S002





S004 · impliesBefore

source roles = [-1, 2, -1, 3]

After

derived = [0, -1, [Yes, No], No, No]

Conditions: none

In the SAME coordinate system,(x,y)=(u,v) IFF x=u AND y=v,equivalently BOTH differences vanish.One matching component or swapped order is insufficient.Derived differences may exceed SAFE while raw inputs remain SAFE.

Step identifiers and dependenciesRule: Coordinate_ORDERED_pair_equality_BOTH_components_SAME_system · Uses: G001, S003









## Reverse checks


- S004 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.
- S003 · premise_and_result_audit — Recompute Coordinate ORIGINAL second component difference y minus v with exact rational arithmetic, not rounded decimals.
- S002 · premise_and_result_audit — Recompute Coordinate ORIGINAL first component difference x minus u with exact rational arithmetic, not rounded decimals.
- S001 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.





## 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: 89ff3705b1a5bf956d0faf064cb44833aae8cb6781de52c6b207a0cf2c5805e5
- candidate record SHA-256: 59d4cd35f6b023bbdfbbe85692b62328bda7a8c810fd881fca27d8a331d38dfb
- semantic review receipt SHA-256: 66bbb31c5fe644576dfd47ac71ca9e367fc23b948eac8e3eb648d96dadea05df
- question-first witness SHA-256: b1e4fbdbca8d0ac3581e2f26466374d870f3c8498fab7cf6873feca5bbec44e7
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20260930-r07-coordinate-point-equality-0010.json)