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.