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R0058-29737 · q-20261006-advance-20261007-r07-geometric-transformations-0037
Use one equal-unit orthonormal Euclidean Cartesian frame. Rotate P=(-1, 12) about the origin counterclockwise by 3 quarter-turns of 90°. Find the image coordinates.
G001 — Use one equal-unit orthonormal Euclidean Cartesian frame. Rotate P=(-1, 12) about the origin counterclockwise by 3 quarter-turns of 90°. 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-quarter-turn-point, quarter_turn_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 CCW turn1 negated old y := sub(0, 12)
After
Transform ORIGINAL CCW turn1 negated old y = -12
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 = [[-1, 12], 3, 0]
After
derived = [[-12, -1]]
Conditions: none
Each step is a90-degree COUNTERCLOCKWISE rotation about the ORIGIN,current(x,y)->(-y,x).Do not change center/direction.The source permits ONLY0..3,not modulo repair of negative counts or4.
Rule: Transform_EACH_ORIGIN_counterclockwise_quarter_turn · Uses: G001, S002
Before
Transform ORIGINAL CCW turn2 negated old y := sub(0, -1)
After
Transform ORIGINAL CCW turn2 negated old y = 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.
Rule: exact_rational_arithmetic · Uses: G001, S003
Before
source roles = [[-1, 12], 3, 1]
After
derived = [[1, -12]]
Conditions: none
Each step is a90-degree COUNTERCLOCKWISE rotation about the ORIGIN,current(x,y)->(-y,x).Do not change center/direction.The source permits ONLY0..3,not modulo repair of negative counts or4.
Rule: Transform_EACH_ORIGIN_counterclockwise_quarter_turn · Uses: G001, S004
Before
Transform ORIGINAL CCW turn3 negated old y := sub(0, -12)
After
Transform ORIGINAL CCW turn3 negated old y = 12
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, S005
Before
source roles = [[-1, 12], 3, 2]
After
derived = [[12, 1]]
Conditions: none
Each step is a90-degree COUNTERCLOCKWISE rotation about the ORIGIN,current(x,y)->(-y,x).Do not change center/direction.The source permits ONLY0..3,not modulo repair of negative counts or4.
Rule: Transform_EACH_ORIGIN_counterclockwise_quarter_turn · Uses: G001, S006
Before
source roles = [[-1, 12], 3]
After
derived = [[12, 1]]
Conditions: none
At n=0 retain the original point;otherwise use exactly the stated updates.This image calculation is not a new formal certificate for a whole-plane theorem.
Rule: Transform_actual_declared_turn_count_including_zero · Uses: G001, S007
S008 · 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.S007 · 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.S006 · premise_and_result_audit — Recompute Transform ORIGINAL CCW turn3 negated old y with exact rational arithmetic, not rounded decimals.S005 · 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.S004 · premise_and_result_audit — Recompute Transform ORIGINAL CCW turn2 negated old y with exact rational arithmetic, not rounded decimals.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 CCW turn1 negated old 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.(12, 1)
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: b67f947919a5db0138c444422a9f504e59bd8ed0117ec84ad1ea766a34bb4ad9candidate record SHA-256: 870f28040514012d0c75b0440b8539fb1e6590e8cad2d7719f7537ce1b972851semantic review receipt SHA-256: 66bbb31c5fe644576dfd47ac71ca9e367fc23b948eac8e3eb648d96dadea05dfquestion-first witness SHA-256: b1e4fbdbca8d0ac3581e2f26466374d870f3c8498fab7cf6873feca5bbec44e7Lean: NOT_RUN · human review: NOT_PERFORMED