Question

graph the image of rectangle tuvw after a rotation 90° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

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

Step2: Identify original coordinates

Assume $T(-8,2)$, $U(0,2)$, $V(0,10)$, $W(-8,10)$.

Step3: Apply rotation rule to point T

For $T(-8,2)$, using $(x,y)\to(-y,x)$, we get $T'(-2, - 8)$.

Step4: Apply rotation rule to point U

For $U(0,2)$, using $(x,y)\to(-y,x)$, we get $U'(-2,0)$.

Step5: Apply rotation rule to point V

For $V(0,10)$, using $(x,y)\to(-y,x)$, we get $V'(-10,0)$.

Step6: Apply rotation rule to point W

For $W(-8,10)$, using $(x,y)\to(-y,x)$, we get $W'(-10,-8)$.

Step7: Graph new points

Plot $T'(-2, - 8)$, $U'(-2,0)$, $V'(-10,0)$, $W'(-10,-8)$ and connect them to form the rotated rectangle.

Answer:

Graph the points $T'(-2, - 8)$, $U'(-2,0)$, $V'(-10,0)$, $W'(-10,-8)$ and connect them to get the image of rectangle $TUVW$ after a 90 - degree counter - clockwise rotation around the origin.