Which algebraic rule describes the 180° counter-clockwise rotation about the origin? a) (x, y) → (−x, y) b) (x, y) → (x, −y) c) (x, y) → (−x, −y) d) (x, y) → (−y, −x)

C

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 180°

a point (x, y ) → (- x, - y) → C

 C) (x, y) → (−x, −y)

Step-by-step explanation:

When we rotate a figure 180°clockwise or counter-clockwise , the magnitude of x and y coordinates remains same but their signs got changed.

For example : After a rotation of 180°clockwise or counter-clockwise (3,4) becomes (-3,-4).

Algebraically , we can say

Ordered pair (x , y ) will become (-x, -y) after a rotation of 180°clockwise or counter-clockwise.

Thus , the algebraic rule describes the 180° counter-clockwise rotation about the origin will be :-

C) (x, y) → (−x, −y)