The question asks: "The center of a figure is located at point (4, 2). What rotation would be required to result in the center being rotated to (-4, -2)?"

To solve this:

1. The original point is $(4, 2)$ and we want it to rotate to $(-4, -2)$.
2. We notice that this transformation looks like a 180-degree rotation around the origin. Why? Because when rotating 180 degrees, both the x- and y-coordinates change sign:
   • $(4, 2) \rightarrow (-4, -2)$.

Thus, the correct answer is 180 degrees, which corresponds to option c.

Would you like more details or have any questions?

Follow-up Questions:

1. What happens when you rotate a point by 90 degrees clockwise?
2. How do you perform a 270-degree rotation about the origin?
3. Can you explain how coordinates change when rotating by 360 degrees?
4. How would you rotate a point by 90 degrees counterclockwise?
5. What is the formula for rotating a point around any arbitrary center?

Tip:

When rotating a point, always check how the coordinates change (sign and position) to ensure you select the right degree of rotation.