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The problem asks for the image of the point \( F(-2, 7) \) after a 180° clockwise rotation. 

To solve this, we can use the formula for rotating a point 180° around the origin. For any point \( (x, y) \), a 180° rotation will map it to \( (-x, -y) \).

### Steps:
- The original point is \( F(-2, 7) \).
- After a 180° clockwise (or counterclockwise, since they are the same for 180°) rotation, the coordinates of the new point will be:
  \[
  F'(-(-2), -(7)) = F'(2, -7)
  \]

So, the image of \( F(-2, 7) \) after a 180° rotation is \( F'(2, -7) \).

The correct answer is **F'(2, -7)** (the orange option).

Would you like more details on the rotation process or any related questions?

Here are 5 related questions to expand on this:
1. How do you perform a 90° clockwise rotation of a point?
2. What would be the image of \( (2, -7) \) after a 270° clockwise rotation?
3. How does a 180° rotation differ from a reflection over the origin?
4. How do rotations affect the orientation of a shape or object?
5. Can you explain the general rule for rotating a point by any angle?

**Tip:** A 180° rotation always maps a point to its opposite quadrant while flipping the signs of both coordinates.

What is the image of F(-2, 7) after a rotation of 180° clockwise?

Learn how to find the image of a point, such as F(-2, 7), after a 180° clockwise rotation. This problem covers key geometry concepts related to coordinate transformations and rotations. Suitable for students in Grades 8-10.

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