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Question 29709: 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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R0058-29709 · q-20261006-advance-20261007-r07-geometric-transformations-0059

Original question and givens

Use one equal-unit orthonormal Euclidean Cartesian frame. Reflect P=(-4, 10) across the x-axis. Find the image coordinates.

  • G001 — Use one equal-unit orthonormal Euclidean Cartesian frame. Reflect P=(-4, 10) across the x-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 x-axis negated y := sub(0, 10)

After

Transform ORIGINAL x-axis negated y = -10

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 = [[-4, 10], x]

After

derived = [[-4, -10]]

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 x-axis 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.

Result

(-4, -10)

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: afff489dee78c8728ff911b98f3884e1b9ef40d138f4129eef43fee4e49716c9
  • candidate record SHA-256: 2e05e86c14b01675bcac20a64944440a7dd19c0c45458b667388669199111231
  • semantic review receipt SHA-256: 66bbb31c5fe644576dfd47ac71ca9e367fc23b948eac8e3eb648d96dadea05df
  • question-first witness SHA-256: b1e4fbdbca8d0ac3581e2f26466374d870f3c8498fab7cf6873feca5bbec44e7
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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