Question

A triangle has vertices at (−2, −2), (−2, −5), and (−4, −5). The triangle is translated 2 units to the right and rotated 90° clockwise about the origin. What are the coordinates of its image?

( , ), ( , ), ( , ) → ( , ), ( , ), ( , ),

Answer 1

Explanation:

translated (shifted) 2 units to the right (positive x direction) creates the points

(-2 + 2, -2) = (0, -2)

(-2 + 2, -5) = (0, -5)

(-4 + 2, -5) = (-2, -5)

and now we rotate these points 90° clockwise around the origin.

that means a positive x turns into a negative y, a negative y into a negative x, a negative x into a positive y, and a positive y into a positive x.

and a 0 just trades places.

therefore,

(0, -2) becomes (-2, 0)

(0, -5) becomes (-5, 0)

(-2, -5) becomes (-5, 2)

so, overall

(-2, -2) becomes (-2, 0)

(-2, -5) becomes (-5, 0)

(-4, -5) becomes (-5, 2)