https://file.aiquickdraw.com/mathbot/file/1730905643381guylnd73.jpg

To determine the coordinates of point \( A' \) after a 180° rotation about the origin, let's go through the steps.

### Steps to Solve
1. **Identify the Original Coordinates of Point A**: Based on the image, it appears that point \( A \) is located at \( (3, 5) \).

2. **Apply the Rotation Transformation**: For a 180° rotation about the origin, the transformation rule is:
   \[
   (x, y) \rightarrow (-x, -y)
   \]
   So, we take the coordinates \( (3, 5) \) and apply this transformation:
   \[
   (3, 5) \rightarrow (-3, -5)
   \]

3. **Verify the Answer**: The new coordinates of \( A' \) after a 180° rotation about the origin would be \( (-3, -5) \).

### Conclusion
The correct answer is:
- \( (-3, -5) \)

Would you like more details on rotation transformations or have any further questions?

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Here are some related questions to expand your understanding:

1. What are the rotation rules for 90° and 270° about the origin?
2. How do the coordinates change with a 180° rotation about a point other than the origin?
3. What is the effect of a 180° rotation on the orientation of a shape?
4. Can you apply a rotation transformation to points in 3D space?
5. How does rotating a point affect its distance from the origin?

**Tip:** For any 180° rotation, simply negate both the x- and y-coordinates of a point.

If you were to rotate ABCD 180° about the origin, what would the coordinate of A' be?

Learn how to determine the new coordinates of point A after a 180° rotation about the origin. This geometry problem uses coordinate transformations and applies the rule (x, y) → (-x, -y) for a 180° rotation, making it suitable for students in Grades 8-10.

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