The problem asks to find the image of a figure after rotating it 180° about the origin. When performing a 180° rotation about the origin on the coordinate plane, the coordinates $(x, y)$ of each point of the figure transform as follows:

$(x, y) \rightarrow (-x, -y)$

This means that each point in the figure will be reflected both horizontally and vertically across the origin.

Let's analyze the options based on this transformation:

• For each vertex $G, F, E, H$ in the original figure, apply the rule $(x, y) \rightarrow (-x, -y)$.
• Then compare the transformed coordinates with the figures in options A, B, C, and D.

The correct answer will be the one where the transformed figure matches the result of applying the 180° rotation rule.

Let me know if you would like me to apply the transformation step-by-step for each point or need further clarification on the process!

Here are 5 related questions to deepen your understanding:

1. What happens when you rotate a figure by 90° instead of 180°?
2. How do coordinates change when rotating a figure by 270° about the origin?
3. Can you describe the effect of reflecting a figure across the y-axis?
4. What is the difference between a rotation and a reflection?
5. How can you verify a figure's rotation algebraically?

Tip: For any rotation about the origin, always visualize the figure's movement to better grasp the transformation rule!