Question

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)

Answer 1

C

Explanation:

Under a counterclockwise rotation about the origin of 180°

a point (x, y ) → (- x, - y) → C

Answer 2

Answer: C) (x, y) → (−x, −y)

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)