Question

identifying points on a pre - image
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)

Explanation:

Step1: Recall rotation rule

The rule for a 270 - degree counter - clockwise rotation about the origin is $(x,y)\to(y, - x)$.

Step2: Identify image points

From the graph, assume the image points are $K'(1, - 3)$, $L'(2,-3)$, $M'(2, - 4)$, $N'(1,-4)$.

Step3: Apply inverse rotation

To find pre - image points, use the inverse rule $(x,y)\to(-y,x)$.
For a point $(x,y)$ in the image, the pre - image point $(x_p,y_p)$ has $x_p=-y$ and $y_p = x$.
If $K'(1,-3)$, then pre - image $K(-3,1)$.
If $L'(2,-3)$, then pre - image $L(-3,2)$.
If $M'(2,-4)$, then pre - image $M(-4,2)$.
If $N'(1,-4)$, then pre - image $N(-4,1)$.
By checking the options, the correct vertices of the pre - image are:

Answer:

M(-3,2)