# Question 8620: Explicit Collinearity

[Return to catalogue page 44](https://ocme.evemisslab.com/en/questions/page/44/)

[← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20260917-point-line-plane/#q-20260917-explicit-collinearity-classification-0020)

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.

R0016-08620 · q-20260917-explicit-collinearity-classification-0020



## Original question and givens

Explicit data: P20, Q20, R20 are not collinear. Are the three points collinear?


- G001 — Explicit data: P20, Q20, R20 are not collinear. Are the three points collinear?





## 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-point-line-plane](https://ocme.evemisslab.com/en/mko/mko-point-line-plane/)





## Step-by-step derivation

S001 · impliesBefore

explicit typed incidence data;no coordinate or visual premise supplied

After

read the stated predicate;absence of a premise is not its negation

Conditions: none

Read the explicit geometric premise without inferring from appearance.An absent premise is not a negative premise;do not invent coordinates or equations.

Step identifiers and dependenciesRule: declared_geometry_not_visual_inference · Uses: G001





S002 · impliesBefore

distinct point labels=[P20, Q20, R20];declared collinear=No;explicit negative=Yes

After

answer=No

Conditions: none

Collinearity means lying on one line,and coplanarity lying in one plane.The positive or negative predicate is explicit here,so answer from that premise,not from labels,drawings or missing data.

Step identifiers and dependenciesRule: declared_same_line_or_plane_predicate · 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: 482e205cef29b7a52766bd8499ef9205c72460041c0e10070d1734f880de3f72
- candidate record SHA-256: 4bc77abd04ebb5b9c6d045e1ff972da8edc306399f56c1ac09eb7cea744b6b83
- semantic review receipt SHA-256: 00fcddb10a9fb0f56697308976a52e68e2537472bd8e68ecbe96d3c4553f4ad2
- question-first witness SHA-256: 198e04380b2d32aef2375b07ca0df1f8afa454d1184993173fad8a3c9187a3d1
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20260917-explicit-collinearity-classification-0020.json)