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R0058-29724 · q-20261006-advance-20261007-r07-geometric-transformations-0074
Use one equal-unit orthonormal Euclidean Cartesian frame. Reflect P=(11, 25) across the line y=−x. Find the image coordinates.
G001 — Use one equal-unit orthonormal Euclidean Cartesian frame. Reflect P=(11, 25) 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
Transform ORIGINAL anti-diagonal negated y := sub(0, 25)
After
Transform ORIGINAL anti-diagonal negated y = -25
Conditions: none
Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
Transform ORIGINAL anti-diagonal negated x := sub(0, 11)
After
Transform ORIGINAL anti-diagonal negated x = -11
Conditions: none
Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
source roles = [[11, 25], anti_diagonal]
After
derived = [[-25, -11]]
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, S003
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 Transform ORIGINAL anti-diagonal negated x with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Recompute Transform ORIGINAL anti-diagonal negated y 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.(-25, -11)
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: 4ca882015a9aa671bca6a30c1a405e64c347857eab806b85db5664378c75f46fcandidate record SHA-256: e5ee474f824422bef3881c61493c06df89b9f305738d6387bf0b6ed23e7e0a2esemantic review receipt SHA-256: 66bbb31c5fe644576dfd47ac71ca9e367fc23b948eac8e3eb648d96dadea05dfquestion-first witness SHA-256: b1e4fbdbca8d0ac3581e2f26466374d870f3c8498fab7cf6873feca5bbec44e7Lean: NOT_RUN · human review: NOT_PERFORMED