Question

Writing a Rule for a Rotation
Based on what you know about rotations, what do you think the mapping rule is for a rotation of 270 degrees clockwise? Explain.

Answer 1

A rotation of 270° clockwise is the same as a rotation of 90° counterclockwise. The standard mapping for a 90° counterclockwise rotation is

(x, y) → (−y, x).

Reason (quick): the basis vectors map as
- (1,0) → (0,1)
- (0,1) → (−1,0)

So x(1,0)+y(0,1) → x(0,1)+y(−1,0) = (−y, x).

Example: (3,2) rotated 270° clockwise → (−2, 3).