Question

graph the image of △stu after a rotation 90° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

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

Step2: Identify original points

Let's assume the coordinates of the vertices of $\triangle STU$ are $S(x_1,y_1)$, $T(x_2,y_2)$, $U(x_3,y_3)$. From the graph, if we assume $S(- 4,-8)$, $T(-4,0)$, $U(-8,-10)$.

Step3: Apply rotation rule to point S

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

Step4: Apply rotation rule to point T

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

Step5: Apply rotation rule to point U

For point $U(-8,-10)$, using the rule $(x,y)\to(-y,x)$, we get $U'=(10,-8)$.

Step6: Graph the new triangle

Plot the points $S'(8, - 4)$, $T'(0,-4)$, $U'(10,-8)$ on the coordinate plane and connect them to form the image of $\triangle STU$ after the 90 - degree counter - clockwise rotation around the origin.

Answer:

Graph the points $S'(8, - 4)$, $T'(0,-4)$, $U'(10,-8)$ and connect them to form the rotated triangle.