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)←←←

Answer is D :)

Answer 1

(x, y) → (y, x) is for reflection about line y=x.
(x, y) → (–y, x) is for 90 deg. counterclockwise rotation (or 270 clockwise)
(x, y) → (y, –x) is for 270 deg. counterclockwise rotation (or 90 clockwise)
(x, y) → (–x, –y) is correct for 180 deg. rotation (clockwise or counterwise)

Answer 2

(x,y) -> (-x,-y)

Explanation:

the mapping rule for a 180° rotation

For example, (2,4) is a point on first quadrant.

When we rotate the point by 180 degree then the point moves to third quadrant.

So (2,4) after rotation by 180 degree becomes (-2,-4)

Mapping rule for (x,y) 180 degree rotation is (-x,-y)

(x,y) -> (-x,-y)