https://file.aiquickdraw.com/mathbot/file/1726683614409o3o7o0ny.jpg

In the given image, we are asked to find the coordinates of point **D** after rotating the figure 180° counterclockwise about the origin.

### Step-by-step process:
1. **Current coordinates of point D:**
   - From the graph, point **D** is located at approximately (-2, -8).

2. **Rotation transformation:**
   - When a point is rotated 180° about the origin, the coordinates \((x, y)\) transform to \((-x, -y)\).
   - Applying this rule to the coordinates of point **D** (-2, -8):
     \[
     (-2, -8) \to (2, 8)
     \]

### Conclusion:
After the 180° counterclockwise rotation, the new coordinates of point **D** are **(2, 8)**.

Would you like further details or clarification? 

Here are 5 related questions to expand on this concept:
1. What happens to the coordinates of a point during a 90° counterclockwise rotation?
2. How would you calculate the new coordinates of a point after a 270° rotation?
3. What are the effects of reflection across the y-axis on the coordinates of a point?
4. How does a translation affect the coordinates of a shape on the coordinate plane?
5. What is the rule for rotating a point 360° around the origin?

**Tip:** For any 180° rotation, simply flip the signs of both the x- and y-coordinates of the point!

The figure below is rotated 180° counterclockwise. What are the coordinates of the image of point D after this transformation?

This page explains how to find the coordinates of point D after a 180° counterclockwise rotation on the coordinate plane. Learn how to apply the transformation rule (x, y) → (-x, -y) to solve this geometry problem. Suitable for students in Grades 7-9.

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