Question

Comparing Rotations
Do you think that a 270° clockwise rotation is the same as a 90° counterclockwise rotation? Explain why or why not.

Answer 1

Yes — they are the same. Rotations are measured modulo 360°, so rotating 270° clockwise (which is −270°) is equivalent to rotating 90° counterclockwise because −270° ≡ 90° (mod 360).

Example: take the point (1, 0).
- 90° counterclockwise sends (1, 0) → (0, 1).
- 270° clockwise also sends (1, 0) → (0, 1).

Algebraically, a 90° counterclockwise rotation maps (x, y) to (−y, x); a 270° clockwise rotation does the same, so they produce identical results.