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 original points

Let's assume the coordinates of points of $\triangle ABC$ are $A(x_1,y_1)$, $B(x_2,y_2)$ and $C(x_3,y_3)$. From the graph, if $A(3, - 6)$, $B(7,-6)$ and $C(3,0)$.

Step3: Apply rotation rule

For point $A(3,-6)$, after rotation, $A'(-3,6)$.
For point $B(7,-6)$, after rotation, $B'(-7,6)$.
For point $C(3,0)$, after rotation, $C'(-3,0)$.

Step4: Graph new points

Plot points $A'(-3,6)$, $B'(-7,6)$ and $C'(-3,0)$ on the coordinate - plane and connect them to form the rotated triangle.

Answer:

Graph the points $A'(-3,6)$, $B'(-7,6)$ and $C'(-3,0)$ and connect them to get the image of $\triangle ABC$ after a 180 - degree counter - clockwise rotation around the origin.