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R0058-29706 · q-20261006-advance-20261007-r07-geometric-transformations-0056
Use one equal-unit orthonormal Euclidean Cartesian frame. Reflect P=(-7, 7) across the y-axis. Find the image coordinates.
G001 — Use one equal-unit orthonormal Euclidean Cartesian frame. Reflect P=(-7, 7) across the y-axis. 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 y-axis negated x := sub(0, -7)
After
Transform ORIGINAL y-axis negated x = 7
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
source roles = [[-7, 7], y]
After
derived = [[7, 7]]
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, S002
S003 · 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.S002 · premise_and_result_audit — Recompute Transform ORIGINAL y-axis negated x 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.(7, 7)
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: a7e194a0bdf35c1133ed1fb5ac7f15c0aa0e3118f13a1458f77ea6703a644e09candidate record SHA-256: 18f0c105d62dd90de713c7bb6de0486b95c90a613759895349f9782cf714ab86semantic review receipt SHA-256: 66bbb31c5fe644576dfd47ac71ca9e367fc23b948eac8e3eb648d96dadea05dfquestion-first witness SHA-256: b1e4fbdbca8d0ac3581e2f26466374d870f3c8498fab7cf6873feca5bbec44e7Lean: NOT_RUN · human review: NOT_PERFORMED