Question

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

Explanation:

Step1: Recall rotation rule

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

Step2: Identify vertices of $\triangle DEF$

Let's assume the coordinates of $D=(3,-7)$, $E=(3,-3)$, $F=(6,-9)$.

Step3: Apply rotation rule to point D

For $D=(3,-7)$, after rotation, $D'=(-7,-3)$.

Step4: Apply rotation rule to point E

For $E=(3,-3)$, after rotation, $E'=(-3,-3)$.

Step5: Apply rotation rule to point F

For $F=(6,-9)$, after rotation, $F'=(-9,-6)$.

Step6: Graph new triangle

Plot points $D'(-7,-3)$, $E'(-3,-3)$, $F'(-9,-6)$ and connect them to form the rotated $\triangle D'E'F'$.

Answer:

Graph the triangle with vertices $(-7,-3)$, $(-3,-3)$, $(-9,-6)$