Question

On a coordinate plane, a rectangle has points K prime (1, 3), L prime (2, 3), M prime (2, negative 3), N prime (1, negative 3).
A rectangle was rotated 270° about the origin.

The image is shown.

Which points are vertices of the pre-image? Check all that apply.

K(–3, –1)
M(–3, 2)
M(3, 2)
N(–3, 1)
N(3, 1)

Answer 1

Rotation 270° CCW maps (x,y) -> (y, -x). Inverting that, a given image (x',y') came from pre-image (x,y) = (-y', x').

Compute from the image vertices:
- K'(1,3) -> pre-image K = (-3,1)
- L'(2,3) -> pre-image L = (-3,2)
- M'(2,-3) -> pre-image M = (3,2)
- N'(1,-3) -> pre-image N = (3,1)

From the choices, the vertices of the pre-image are M(3, 2) and N(3, 1).