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In the provided problem, you are asked to perform a 180° rotation of a line segment about the origin. To solve this, here is the step-by-step process for rotating any point or line segment by 180°:

### Steps for a 180° rotation about the origin:
1. **Identify the coordinates of the endpoints** of the line segment.
   - Let the endpoints of the original line segment be \( (x_1, y_1) \) and \( (x_2, y_2) \).

2. **Apply the 180° rotation rule**:
   - For any point \( (x, y) \), after a 180° rotation about the origin, the new coordinates will be \( (-x, -y) \).

3. **Find the new coordinates** of the endpoints after rotation:
   - If the original coordinates are \( (x_1, y_1) \), after rotation, the new point will be \( (-x_1, -y_1) \).
   - Similarly, for \( (x_2, y_2) \), the new point will be \( (-x_2, -y_2) \).

4. **Plot the new points** on the graph to complete the rotated line segment.

### In your graph:
- From the image, the line segment appears to be between approximately the points \( (-3, 2) \) and \( (-1, 5) \).
  
### Applying the 180° rotation:
- Point \( (-3, 2) \) after a 180° rotation becomes \( (3, -2) \).
- Point \( (-1, 5) \) after a 180° rotation becomes \( (1, -5) \).

### Final result:
- You should plot the line segment connecting the points \( (3, -2) \) and \( (1, -5) \) on the graph.

Would you like a further explanation or have questions about any part of the process?

Here are 5 related questions to deepen understanding:
1. What happens to a point under a 90° rotation about the origin?
2. How would the coordinates change for a 270° rotation about the origin?
3. What is the general rule for rotating a point by any angle \( \theta \)?
4. How do you rotate figures that are not centered on the origin?
5. Can a 180° rotation be considered a reflection in some cases?

**Tip:** When performing rotations, always remember to change the signs of both coordinates for a 180° rotation!

Draw the following segment after a 180° rotation about the origin.

Learn how to rotate a line segment by 180° around the origin in a coordinate plane. This geometry problem involves understanding rotation transformations, with the formula (x, y) → (-x, -y). Perfect for students in Grades 8-10.

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