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 rotation rule

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

Step2: Let the coordinates of $Q$ be $(x,y)$

If $Q(x,y)$ is rotated $90^{\circ}$ counter - clockwise about the origin to get $Q'(-3,4)$. Then using the rule $(-y,x)=(-3,4)$.

Step3: Solve for $x$ and $y$

We have $-y=-3$ and $x = 3$. So $y = 3$ and $x=4$. Thus the coordinates of $Q$ are $(4,3)$.

Answer:

D. $(4, 3)$