Question

graph the image of △abc after a rotation 180° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

The rule for a 180 - degree counter - clockwise rotation around the origin is $(x,y)\to(-x,-y)$.

Step2: Identify vertices of $\triangle ABC$

Let's assume the coordinates of $A=(2, - 8)$, $B=(6,-8)$, $C=(0,-4)$.

Step3: Apply rotation rule to point A

For $A=(2,-8)$, after rotation, $A'=(-2,8)$.

Step4: Apply rotation rule to point B

For $B=(6,-8)$, after rotation, $B'=(-6,8)$.

Step5: Apply rotation rule to point C

For $C=(0,-4)$, after rotation, $C'=(0,4)$.

Step6: Graph the new triangle

Plot points $A'(-2,8)$, $B'(-6,8)$ and $C'(0,4)$ and connect them to form $\triangle A'B'C'$.

Answer:

Graph $\triangle A'B'C'$ with vertices $A'(-2,8)$, $B'(-6,8)$ and $C'(0,4)$.