Question

Trapezoid ABCD is shown. Trapezoid ABCD is rotated 90° clockwise. What rule shows the input and output of the rotation, and what is the new coordinate of A'?

a. (x, y) → (−x, −y); A' is at (5, −1)

b. (x, y) → (−y, x); A' is at (−1, −5)

c. (x, y) → (y, −x); A' is at (1, 5)

d. (x, y) → (x, −y); A' is at (−5, −1)

Answer 1

The rule that shows the input and output of the rotation is (x, y) → (y, -x). The new coordinate of A' is (-1, -5).

Step-by-step explanation:

When a trapezoid ABCD is rotated 90° clockwise, the rule that shows the input and output of the rotation is (x, y) → (y, -x). This means that the x-coordinate becomes the y-coordinate and the y-coordinate becomes the negative of the x-coordinate.

Given that A is at (5, -1), we can apply the rule to find the new coordinate of A':

A' = (y, -x) = (-1, -(5)) = (-1, -5).