Question

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

Explanation:

Step1: Recall rotation rule

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

Step2: Identify original vertices

Let's assume the coordinates of the vertices of $\triangle RST$ are $R(x_1,y_1)$, $S(x_2,y_2)$ and $T(x_3,y_3)$. From the graph, if we assume $R(8,-8)$, $S(8, - 4)$, $T(2,-8)$.

Step3: Apply rotation rule to $R$

For point $R(8,-8)$, after rotation, the new coordinates $R'(y_1,-x_1)=(-8,-8)$.

Step4: Apply rotation rule to $S$

For point $S(8, - 4)$, after rotation, the new coordinates $S'(-4,-8)$.

Step5: Apply rotation rule to $T$

For point $T(2,-8)$, after rotation, the new coordinates $T'(-8,-2)$.

Step6: Graph new triangle

Plot the points $R'(-8,-8)$, $S'(-4,-8)$ and $T'(-8,-2)$ and connect them to form the rotated triangle.

Answer:

Graph the triangle with vertices $(-8,-8)$, $(-4,-8)$ and $(-8,-2)$.