Question

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 $(x,y)\to(y, - x)$. To find the pre - image, we use the reverse rule $(x,y)\to(-y,x)$.

Step2: Identify vertices of the image

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

Step3: Apply the reverse rotation rule

For a point $(x,y)$ of the image, the pre - image point $(x_p,y_p)$ is given by $x_p=-y$ and $y_p = x$.
For $K'(1,3)$: Pre - image is $K(-3,1)$.
For $L'(2,3)$: Pre - image is $L(-3,2)$.
For $M'(2, - 1)$: Pre - image is $M(1,2)$.
For $N'(1, - 1)$: Pre - image is $N(1,1)$.
Comparing with the given options, the correct vertices of the pre - image are $M(-3,2)$.

Answer:

B. $M(-3,2)$