It seems like you've uploaded the same image again. I’ve already provided the explanation for the two questions:

1. Plotting point R: The center of rotation, point R, should be the midpoint between P and Q. This ensures that a 180° rotation about point R moves point P onto point Q.

2. Is there more than one point R that works?: No, only the midpoint between P and Q will work as the center of a 180° rotation that maps P onto Q. Any other point would not create this direct transformation.

Would you like any further clarifications, or would you like me to provide a step-by-step process for solving this visually?

Here are 5 related questions to expand your understanding:

1. What is the formula for finding the midpoint between two points on a coordinate plane?
2. How does rotating a point 90° differ from rotating it 180° around a center?
3. If point R is placed incorrectly, what would the result of the 180° rotation look like?
4. How do we apply the concept of rotation in 3D space, as opposed to the 2D line in this problem?
5. What other transformations (e.g., reflection) can map point P onto point Q?

Tip: For rotations, always visualize or calculate the midpoint for a 180° transformation, as it's essential for finding the correct center point.