Question

graph the image of rectangle stuv after a rotation 270° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

The rule for a 270 - counter - clockwise rotation around the origin is $(x,y)\to(y, - x)$.

Step2: Find coordinates of vertices of rectangle after rotation

Let's assume the coordinates of the vertices of rectangle $STUV$ are: $S(-6,-9)$, $T(-4,-9)$, $U(-4,-2)$, $V(-6,-2)$.
For point $S(-6,-9)$: After rotation, $S'(-9,6)$.
For point $T(-4,-9)$: After rotation, $T'(-9,4)$.
For point $U(-4,-2)$: After rotation, $U'(-2,4)$.
For point $V(-6,-2)$: After rotation, $V'(-2,6)$.

Step3: Graph the new rectangle

Plot the points $S'(-9,6)$, $T'(-9,4)$, $U'(-2,4)$, $V'(-2,6)$ on the coordinate - plane and connect them to form the new rectangle.

Answer:

Graph the rectangle with vertices $(-9,6)$, $(-9,4)$, $(-2,4)$, $(-2,6)$.