https://file.aiquickdraw.com/mathbot/file/17285042510357ryooekr.jpg

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

When you rotate a point \( (x, y) \) by 180° clockwise (or counterclockwise, since a 180° rotation is the same in both directions), the new coordinates are given by \( (-x, -y) \).

For the point \( F(-2, 7) \):
- The new \( x \)-coordinate becomes \( -(-2) = 2 \).
- The new \( y \)-coordinate becomes \( -(7) = -7 \).

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

So, the correct answer is **F'(2, -7)**.

Would you like more details or have any other questions?

### 5 Related Questions:
1. What happens to a point after a 90° clockwise rotation?
2. How do you determine the new coordinates after a 270° counterclockwise rotation?
3. How is the formula for a 180° rotation derived?
4. What is the effect of a 360° rotation on a point's coordinates?
5. How do different types of transformations (e.g., reflections, translations) affect coordinates?

### Tip:
For any rotation by \( \theta \) degrees, you can use trigonometric formulas for more complex cases, but remember that 90°, 180°, and 270° rotations have simple coordinate transformation rules.

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

Learn how to determine the image of point F(-2, 7) after a 180° clockwise rotation. This problem explores the concepts of coordinate geometry and rotation transformations. Suitable for students in Grades 8-10.

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