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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.

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)?

Solve the geometry problem involving a 180-degree rotation. Learn how to rotate a point (4, 2) around the origin to get (-4, -2), covering key concepts of coordinate geometry and rotation transformations. Suitable for students in Grades 8-10.

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