Question

graph the image of rectangle stuv after a rotation 270° counter - clockwise around the origin.

Explanation:

Step1: Recall rotation rule

The rule for a 270 - counter - clockwise rotation about the origin for a point $(x,y)$ is $(y, - x)$.

Step2: Let's assume rectangle STUV has vertices $S(x_1,y_1)$, $T(x_2,y_2)$, $U(x_3,y_3)$, $V(x_4,y_4)$

For vertex $S(x_1,y_1)$, the new vertex $S'(y_1,-x_1)$ after 270 - counter - clockwise rotation about the origin. Similarly, for $T(x_2,y_2)$ the new vertex is $T'(y_2,-x_2)$, for $U(x_3,y_3)$ the new vertex is $U'(y_3,-x_3)$ and for $V(x_4,y_4)$ the new vertex is $V'(y_4,-x_4)$.

Step3: Plot new vertices

Plot the new vertices $S'$, $T'$, $U'$, $V'$ on the coordinate - plane and connect them in order to form the rotated rectangle.

Answer:

Graph the new rectangle formed by the vertices obtained using the rotation rule $(x,y)\to(y, - x)$ for each vertex of rectangle STUV.