Question

graph the image of $\triangle abc$ after a rotation $180^{\circ}$ counterclockwise around the origin.

Explanation:

Step1: Identify original coordinates

From the graph:
$A=(2, -8)$, $B=(5, -9)$, $C=(0, -3)$

Step2: Apply 180° rotation rule

A 180° counterclockwise rotation around the origin transforms a point $(x,y)$ to $(-x,-y)$.
For $A$: $(-2, -(-8))=(-2, 8)$
For $B$: $(-5, -(-9))=(-5, 9)$
For $C$: $(-0, -(-3))=(0, 3)$

Step3: Plot new points

Plot $A'=(-2, 8)$, $B'=(-5, 9)$, $C'=(0, 3)$ and connect them to form $\triangle A'B'C'$.

Answer:

The image $\triangle A'B'C'$ has vertices at $A'(-2, 8)$, $B'(-5, 9)$, and $C'(0, 3)$. When these points are plotted and connected on the coordinate grid, they form the rotated triangle.