After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are a'(6, 3), b'(-2, 1),
and c'(1,7). what are the coordinates of the vertices of the pre-image?

A(-3, 6), B(-1, -2), C(-7, 1)

Step-by-step explanation:

To the pre-image after a 270°-counterclockwise rotation [90°-clockwise rotation], just reverse it by doing a 270°-clockwise rotation [90°-counterclockwise rotation]:

Extended Rotation Rules

So, perform your rotation:

270°-clockwise rotation [90°-counterclockwise rotation] → C'[1, 7] was originally at C[-7, 1]

→ B'[-2, 1] was originally at B[-1, -2]

→ A'[6, 3] was originally at A[-3, 6]

I am joyous to assist you anytime.