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R0058-29753 · q-20261006-advance-20261007-r07-geometric-transformations-0003
Use one equal-unit orthonormal Euclidean Cartesian frame. The point is P=(-10, -1) and translation vector t=[1, 2]. Find the coordinates of P+t.
G001 — Use one equal-unit orthonormal Euclidean Cartesian frame. The point is P=(-10, -1) and translation vector t=[1, 2]. Find the coordinates of P+t.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-translation-point, translation_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 translation coordinate0 := sum(-10, 1)
After
Transform ORIGINAL translation coordinate0 = -9
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 translation coordinate1 := sum(-1, 2)
After
Transform ORIGINAL translation coordinate1 = 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, S002
Before
source roles = [[-10, -1], [1, 2]]
After
derived = [[-9, 1]]
Conditions: none
In the SAME origin/basis,add each original translation component to obtain the ACTUAL image.Returning only v is not P+t.Derived sums may exceed SAFE while raw inputs remain SAFE.
Rule: Transform_translation_ACTUAL_image_not_only_displacement · 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 translation coordinate1 with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Recompute Transform ORIGINAL translation coordinate0 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.(-9, 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: 7021bb850b520e2b8347d824c4d1dc9a7c62ed5cd30122b313c1efbbf6b13ca8candidate record SHA-256: befc4826ed68a1e3f6c25ef2e82311d128e11af9a29a450c0334d9d739d46890semantic review receipt SHA-256: 66bbb31c5fe644576dfd47ac71ca9e367fc23b948eac8e3eb648d96dadea05dfquestion-first witness SHA-256: b1e4fbdbca8d0ac3581e2f26466374d870f3c8498fab7cf6873feca5bbec44e7Lean: NOT_RUN · human review: NOT_PERFORMED