Question

graph the image of trapezoid stuv after a reflection over the line y = -x.

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ over the line $y = -x$ is $(x,y)\to(-y,-x)$.

Step2: Assume trapezoid vertices

Suppose the vertices of trapezoid $STUV$ are $S(x_1,y_1)$, $T(x_2,y_2)$, $U(x_3,y_3)$, $V(x_4,y_4)$.

Step3: Find new - coordinates

The reflected vertices will be $S'( - y_1,-x_1)$, $T'( - y_2,-x_2)$, $U'( - y_3,-x_3)$, $V'( - y_4,-x_4)$.

Step4: Plot new trapezoid

Plot the points $S'$, $T'$, $U'$, $V'$ on the coordinate - plane and connect them in order to get the reflected trapezoid.

Since the original coordinates of trapezoid $STUV$ are not given, we can't give the exact numerical coordinates of the reflected trapezoid. But the general method is as above. If we assume $S(-8, - 10)$, $T(8,-10)$, $U(4,-8)$, $V(2,-8)$:

For point $S$

Step1: Apply reflection rule

$S(-8,-10)\to S'(10,8)$.

For point $T$

Step1: Apply reflection rule

$T(8,-10)\to T'(10,-8)$.

For point $U$

Step1: Apply reflection rule

$U(4,-8)\to U'(8,-4)$.

For point $V$

Step1: Apply reflection rule

$V(2,-8)\to V'(8,-2)$.
Then plot the points $S'(10,8)$, $T'(10,-8)$, $U'(8,-4)$, $V'(8,-2)$ and connect them to get the reflected trapezoid.

Answer:

Plot the points obtained by applying the rule $(x,y)\to(-y,-x)$ to the vertices of trapezoid $STUV$ and connect them to form the reflected trapezoid. If $S(-8, - 10)$, $T(8,-10)$, $U(4,-8)$, $V(2,-8)$, the reflected points are $S'(10,8)$, $T'(10,-8)$, $U'(8,-4)$, $V'(8,-2)$ and connect these new points.