Question

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)

Explanation:

A 180° rotation around the origin inverts the sign of both the x and y coordinates of a point. The other options correspond to different transformations: $(x,y)\to(y,x)$ is a reflection over $y=x$, $(x,y)\to(-y,x)$ is a 90° counterclockwise rotation, and $(x,y)\to(y,-x)$ is a 90° clockwise rotation.

Answer:

$\boldsymbol{(x, y)
ightarrow (-x, -y)}$