Question

Rectangle MNPQ is rotated using the origin as the center of rotation, resulting in rectangle M’N’P’Q’, as shown below.

On a coordinate plane, rectangle M N P Q has points (negative 2, 6), (0, 4), (negative 3, 1), (negative 5, 3). Rectangle M prime N prime P prime Q prime has points (6, 2), (4, 0), (1, 3), (3, 5).

Which rotation may have occurred?
a 45° rotation clockwise
a 45° rotation counterclockwise
a 90° rotation clockwise
a 90° rotation counterclockwise

Answer 1

90° rotation clockwise.

Reason: A 90° clockwise rotation about the origin maps (x,y) → (y, −x).
Applying to the given points: (−2,6) → (6,2), (0,4) → (4,0), (−3,1) → (1,3), (−5,3) → (3,5), which match M′N′P′Q′.