Question 29746: Counterclockwise Quarter-Turns about the Origin

Original question and givens

Use one equal-unit orthonormal Euclidean Cartesian frame. Rotate P=(8, 21) 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, 21) 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, 21], 0]

derived = [[8, 21]]

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, 21)

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.