A point P(5, 1) is rotated by 90° about a pivot point (2, 2). What is the…
20162022
A point P(5, 1) is rotated by 90° about a pivot point (2, 2). What is the coordinate of new transformed point P′ ?
- A.
(3, 5)
- B.
(5, 3)
- C.
(2, 4)
- D.
(1, 5)
Attempted by 45 students.
Show answer & explanation
Correct answer: A
Key insight: To rotate a point about a pivot, first translate the point so the pivot is at the origin, apply the rotation, then translate back.
Step 1: Translate the point by subtracting the pivot: (5, 1) − (2, 2) = (3, −1).
Step 2: Rotate 90° counterclockwise using the rule (x, y) → (−y, x): (3, −1) → (1, 3).
Step 3: Translate back by adding the pivot: (1, 3) + (2, 2) = (3, 5).
Final answer: (3, 5).