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 rule

To find the pre - image of a point $(x',y')$ after a 90 - degree counter - clockwise rotation, we use the inverse rule $(x',y')\to(y', - x')$.
For point $Q'(-3,4)$, applying the inverse rule:
Let $x'=-3$ and $y' = 4$. Then the pre - image $x = y'=4$ and $y=-x' = 3$.

Answer:

D. $(4,3)$