Question

write the coordinates of the vertices after a rotation 90° counterclockwise around the origin. q ( , ) r ( , ) s ( , ) t ( , )

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation around the origin is $(x,y)\to(-y,x)$.

Step2: Find coordinates of Q

The coordinates of $Q$ are $(-6,-9)$. Using the rotation rule, $x=-6$ and $y = - 9$. Then $x'=-(-9)=9$ and $y'=-6$. So $Q'=(9,-6)$.

Step3: Find coordinates of R

The coordinates of $R$ are $(-6,-3)$. Using the rotation rule, $x=-6$ and $y=-3$. Then $x'=-(-3)=3$ and $y'=-6$. So $R'=(3,-6)$.

Step4: Find coordinates of S

The coordinates of $S$ are $(-1,-3)$. Using the rotation rule, $x=-1$ and $y=-3$. Then $x'=-(-3)=3$ and $y'=-1$. So $S'=(3,-1)$.

Step5: Find coordinates of T

The coordinates of $T$ are $(-1,-9)$. Using the rotation rule, $x=-1$ and $y=-9$. Then $x'=-(-9)=9$ and $y'=-1$. So $T'=(9,-1)$.

Answer:

$Q'(9,-6)$
$R'(3,-6)$
$S'(3,-1)$
$T'(9,-1)$