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: Analyze point $K'$

Assume $K'(1, - 3)$. Using the reverse rotation rule $(-y,x)$, the pre - image of $K'$ is $K(-3,-1)$.

Step3: Analyze point $L'$

Assume $L'(1, - 1)$. The pre - image using the reverse rule is $L(-1,-1)$.

Step4: Analyze point $M'$

Assume $M'(2,-3)$. The pre - image is $M(-3,2)$.

Step5: Analyze point $N'$

Assume $N'(2,-1)$. The pre - image is $N(-1,-1)$.

Answer:

K(-3, -1), M(-3, 2)