Question

a rectangle is transformed according to the rule $r_{0,90^{circ}}$. the image of the rectangle has vertices located at $r(-4, 4), s(-4, 1), p(-3, 1),$ and $q(-3, 4)$. what is the location of q?
(-4, -3)
(-3, -4)
(3, 4)
(4, 3)

Explanation:

Step1: Recall 90 - degree rotation rule

The rule for a 90 - degree counter - clockwise rotation about the origin $R_{0,90^{\circ}}$ is $(x,y)\to(-y,x)$.

Step2: Apply the inverse rotation rule

To find the original point $Q$ from its image $Q'(-3,4)$, we use the inverse rule. If $(x',y')$ is the image after a 90 - degree counter - clockwise rotation and $(x,y)$ is the pre - image, then $x = y'$ and $y=-x'$.
For $Q'(-3,4)$, $x = 4$ and $y = 3$.

Answer:

D. $(4,3)$