Question

graph the image of △rst after a rotation 270° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

The rule for a 270 - degree counter - clockwise rotation around the origin is $(x,y)\to(y, - x)$.

Step2: Identify vertices of $\triangle{RST}$

Let's assume the coordinates of the vertices of $\triangle{RST}$ are $R(x_1,y_1)$, $S(x_2,y_2)$, $T(x_3,y_3)$. From the graph, if we assume $R(8,-8)$, $S(8,-3)$, $T(2,-8)$.

Step3: Apply rotation rule to $R$

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

Step4: Apply rotation rule to $S$

For point $S(8,-3)$, using the rule $(x,y)\to(y, - x)$, we get $S'(-3,-8)$.

Step5: Apply rotation rule to $T$

For point $T(2,-8)$, using the rule $(x,y)\to(y, - x)$, we get $T'(-8,-2)$.

Step6: Graph the new triangle

Plot the points $R'(-8,-8)$, $S'(-3,-8)$, $T'(-8,-2)$ and connect them to form the rotated triangle $\triangle{R'S'T'}$.

Answer:

Graph the points $(-8,-8)$, $(-3,-8)$, $(-8,-2)$ and connect them to form the image of $\triangle{RST}$ after a 270 - degree counter - clockwise rotation around the origin.