To rotate the figure with points $A(2,0)$, $B(-1,-2)$, and $C(2,-2)$ 180 degrees around the origin, you need to apply the transformation $(x, y)$ → $(-x, -y)$ to each point.

• Point $A(2,0)$ becomes $A'(-2,0)$.
• Point $B(-1,-2)$ becomes $B'(1,2)$.
• Point $C(2,-2)$ becomes $C'(-2,2)$.

So, the points of the image are:

• $A'(-2,0)$
• $B'(1,2)$
• $C'(-2,2)$

Would you like more details on how rotations work or have any other questions?

Here are 5 related questions:

1. How would you rotate a point 90 degrees counterclockwise around the origin?
2. What are the coordinates of point $D(-3,4)$ after a 180-degree rotation around the origin?
3. How does rotating a figure 270 degrees clockwise compare to rotating it 90 degrees counterclockwise?
4. What is the general formula for rotating a point $(x,y)$ by $\theta$ degrees around the origin?
5. How does reflecting a point over the y-axis differ from rotating it 180 degrees around the origin?

Tip: When rotating a point 180 degrees around the origin, the coordinates simply switch signs.