Question

graph the image of △tuv after a rotation 270° clockwise around the origin.

Explanation:

Step1: Recall rotation rule

A 270 - degree clockwise rotation around the origin has the rule $(x,y)\to(y, - x)$.

Step2: Identify original coordinates

The coordinates of the vertices of $\triangle TUV$ are: $T(0,4)$, $U(8,4)$, $V(0,9)$.

Step3: Apply rotation rule to point T

For $T(0,4)$, using the rule $(x,y)\to(y, - x)$, we get $T'(4,0)$.

Step4: Apply rotation rule to point U

For $U(8,4)$, using the rule $(x,y)\to(y, - x)$, we get $U'(4,-8)$.

Step5: Apply rotation rule to point V

For $V(0,9)$, using the rule $(x,y)\to(y, - x)$, we get $V'(9,0)$.

Step6: Graph the new triangle

Plot the points $T'(4,0)$, $U'(4,-8)$, $V'(9,0)$ and connect them to form the image of $\triangle TUV$ after the 270 - degree clockwise rotation.

Answer:

Graph the points $T'(4,0)$, $U'(4,-8)$, $V'(9,0)$ and connect them to form the rotated triangle.