https://file.aiquickdraw.com/mathbot/file/1726192209793no3bx0ib.jpg

To solve this, we need to rotate the line segment \( CD \) by 180 degrees around point \( E \).

### Rotation by 180 degrees:
- When we rotate a point or a segment 180° around another point, the result is that each point on the segment ends up directly opposite to its starting position, at the same distance from the center of rotation. 
- Essentially, if we reflect each point through the center of rotation, we get the rotated figure.

### Steps for rotating segment \( CD \):
1. **Identify Coordinates**: Suppose the coordinates of \( C \), \( D \), and \( E \) are known (or assume they can be plotted). The midpoint \( M \) of segment \( CD \) is not relevant for this rotation but indicates the center of the segment.
2. **Rotate Points**: 
   - Rotate point \( C \) around \( E \) by 180°.
   - Rotate point \( D \) around \( E \) by 180°.
   - The new positions of \( C \) and \( D \) will be directly opposite their current positions relative to point \( E \), forming a new segment.

Since this is a purely geometric operation (180° rotation results in a straight line opposite), the rotated segment \( CD \) would flip entirely over point \( E \).

Would you like more details or a step-by-step drawing approach? 

Here are 5 related questions:
1. How would the image change if we rotated by 90° instead of 180°?
2. What are the general rules for rotating a point around another point?
3. How do you calculate the new coordinates of a point after rotation?
4. What happens to the distance between points during a 180° rotation?
5. How do you define the direction of rotation (clockwise vs. counterclockwise)?

**Tip:** For 180° rotations, the new coordinates of any point \( (x, y) \) become \( (-x, -y) \) relative to the center of rotation.

Use the sketch tool to rotate segment CD 180° around point E.

Learn how to rotate the line segment CD by 180° around a point E using geometric principles. This problem involves understanding the rotation theorem and applying formulas for finding the new coordinates of points after a 180-degree rotation.

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