Question 29730: Counterclockwise Quarter-Turns about the Origin

Original question and givens

Use one equal-unit orthonormal Euclidean Cartesian frame. Rotate P=(-8, 5) about the origin counterclockwise by 0 quarter-turns of 90°. Find the image coordinates.

• G001 — Use one equal-unit orthonormal Euclidean Cartesian frame. Rotate P=(-8, 5) about the origin counterclockwise by 0 quarter-turns of 90°. 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.

• mko-geometric-transformations

Step-by-step derivation

source roles = [qf-transform-quarter-turn-point, quarter_turn_point]

derived = [[image_POINT_string]]

source roles = [[-8, 5], 0]

derived = [[-8, 5]]

Reverse checks

• S002 · 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.
• 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

(-8, 5)

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.