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R0058-29711 · q-20261006-advance-20261007-r07-geometric-transformations-0061
Use one equal-unit orthonormal Euclidean Cartesian frame. Reflect P=(-2, 12) across the line y=x. Find the image coordinates.
G001 — Use one equal-unit orthonormal Euclidean Cartesian frame. Reflect P=(-2, 12) across the line y=x. Find the image coordinates.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.
Before
source roles = [qf-transform-axis-reflection-point, axis_reflection_point]
After
derived = [[image_POINT_string]]
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.
Rule: R58_EXACT_source_interface_and_answer_ROLE · Uses: G001
Before
source roles = [[-2, 12], diagonal]
After
derived = [[12, -2]]
Conditions: none
The FOUR declared axes give(x,-y),(-x,y),(y,x),(-y,-x),keeping the parallel component and reversing the perpendicular one.Do not confuse a line reflection with central inversion.
Rule: Transform_exact_DECLARED_reflection_axis_formula · Uses: G001, S001
S002 · 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.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.(12, -2)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
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.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: f0377cf4a26229259df035f15a7e21e5d9bf132c600f5fdc46345853fdf5ce21candidate record SHA-256: 854ce3d24e5c23a424058a48841d9d111f4a63b2dce53cbb085bc9c502c12728semantic review receipt SHA-256: 66bbb31c5fe644576dfd47ac71ca9e367fc23b948eac8e3eb648d96dadea05dfquestion-first witness SHA-256: b1e4fbdbca8d0ac3581e2f26466374d870f3c8498fab7cf6873feca5bbec44e7Lean: NOT_RUN · human review: NOT_PERFORMED