Question

the coordinates of the vertices of a quadrilateral are s (-1,3), t (-1,6), v (-2,6), and w (-2,3). quadrilateral stvw is rotated 90° clockwise with the origin as the center of rotation to create quadrilateral stvw. which graph correctly shows quadrilateral stvw?

Explanation:

Step1: Recall rotation rule

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

Step2: Apply rule to point S

For $S(-1,3)$, using the rule $(x,y)\to(y, - x)$, we get $S'(3,1)$.

Step3: Apply rule to point T

For $T(-1,6)$, using the rule $(x,y)\to(y, - x)$, we get $T'(6,1)$.

Step4: Apply rule to point V

For $V(-2,6)$, using the rule $(x,y)\to(y, - x)$, we get $V'(6,2)$.

Step5: Apply rule to point W

For $W(-2,3)$, using the rule $(x,y)\to(y, - x)$, we get $W'(3,2)$.

Answer:

We need to check which graph has vertices $S'(3,1)$, $T'(6,1)$, $V'(6,2)$ and $W'(3,2)$. Without seeing the full set of graphs to choose from, we have found the new - coordinates of the rotated quadrilateral. If we assume we are choosing from the two given graphs with points labeled, we would pick the graph with the points in the correct positions based on the calculated coordinates.