Question

Describing the Mapping for 180° Rotations
What is the mapping rule for a 180° rotation?

(x, y) → (y, x)
(x, y) → (–y, x)
(x, y) → (y, –x)
(x, y) → (–x, –y)

Answer 1

A 180° rotation about the origin sends every point (x, y) to (−x, −y).
So the correct mapping is (x, y) → (−x, −y).

(You can see this from the rotation matrix with θ = 180°: [[−1, 0], [0, −1]].)