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Question 29710: Reflection across a Specified Line through the Origin

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0058-29710 · q-20261006-advance-20261007-r07-geometric-transformations-0060

Original question and givens

Use one equal-unit orthonormal Euclidean Cartesian frame. Reflect P=(-3, 11) across the y-axis. Find the image coordinates.

  • G001 — Use one equal-unit orthonormal Euclidean Cartesian frame. Reflect P=(-3, 11) across the y-axis. Find the image coordinates.

Definition and scope

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.

Step-by-step derivation

S001 · implies

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.

Step identifiers and dependencies

Rule: R58_EXACT_source_interface_and_answer_ROLE · Uses: G001

S002 · calculation

Before

Transform ORIGINAL y-axis negated x := sub(0, -3)

After

Transform ORIGINAL y-axis negated x = 3

Conditions: none

Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S001

S003 · implies

Before

source roles = [[-3, 11], y]

After

derived = [[3, 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.

Step identifiers and dependencies

Rule: Transform_exact_DECLARED_reflection_axis_formula · Uses: G001, S002

Reverse checks

  • 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.

Result

(3, 11)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

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.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: e3f121d392aca32656b345f4ac6d4cbae523651723577fe9cf7894a8a9634eb0
  • candidate record SHA-256: a9699b4e2a3bb337655cc6d74f7d03a07f9662bab19569660d038b0a0aced9e1
  • semantic review receipt SHA-256: 66bbb31c5fe644576dfd47ac71ca9e367fc23b948eac8e3eb648d96dadea05df
  • question-first witness SHA-256: b1e4fbdbca8d0ac3581e2f26466374d870f3c8498fab7cf6873feca5bbec44e7
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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