Question

graph the image of rectangle tuvw after a rotation 180° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

The rule for a 180 - degree counter - clockwise rotation around the origin is $(x,y)\to(-x,-y)$.

Step2: Identify original coordinates

Assume $T(5,1)$, $U(8,1)$, $V(8,9)$, $W(5,9)$.

Step3: Apply rotation rule

For point $T(5,1)$, the new point $T'$ is $(- 5,-1)$.
For point $U(8,1)$, the new point $U'$ is $(-8,-1)$.
For point $V(8,9)$, the new point $V'$ is $(-8,-9)$.
For point $W(5,9)$, the new point $W'$ is $(-5,-9)$.

Step4: Graph the new rectangle

Plot the points $T'(-5,-1)$, $U'(-8,-1)$, $V'(-8,-9)$, $W'(-5,-9)$ and connect them to form the new rectangle.

Answer:

Graph the rectangle with vertices $(-5,-1)$, $(-8,-1)$, $(-8,-9)$, $(-5,-9)$