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To find the coordinates of the center of rotation that maps triangle \( R \) onto triangle \( R' \) after a 90° clockwise rotation, we can follow a step-by-step geometric analysis. Here's how we proceed:

1. **Identifying corresponding points**:
   We observe that a 90° clockwise rotation maps each vertex of triangle \( R \) to its corresponding vertex in triangle \( R' \). If we can determine where each vertex of \( R \) goes, we can begin to track the path of the rotation.

2. **Using perpendicularity of 90° rotation**:
   A 90° clockwise rotation ensures that the line segments from the center of rotation to each vertex of the triangle are perpendicular before and after the rotation. This means that the triangles share a common center of rotation.

3. **Midpoint property**:
   The midpoint of any line segment connecting a point in \( R \) to its corresponding point in \( R' \) will lie on the line containing the center of rotation. By finding the midpoints of these corresponding points, we can find the location of the center.

4. **Solving geometrically**:
   Based on the diagram, triangle \( R \) is at a higher position than triangle \( R' \), and both appear to be rotated around a specific point between them. Using the concept of perpendicular bisectors or symmetry, we conclude that the center of rotation is the point (4, 4).

Thus, the coordinates of the center of rotation are:

\[
\boxed{(4, 4)}
\]

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Would you like to see the geometric proof in detail, or do you have any questions?

Here are five related questions:
1. How do we confirm that a 90° rotation preserves the distance between corresponding points?
2. What are the rules for rotating points by 90° around a given center?
3. Can you perform a similar rotation in the counterclockwise direction? What changes?
4. How can you calculate the rotation matrix for 90° clockwise rotation?
5. How does the concept of rotational symmetry apply to polygons?

**Tip**: When performing rotations, always ensure that the angle is measured correctly with respect to the positive or negative direction (clockwise or counterclockwise).

A rotation of 90° clockwise maps triangle R onto triangle R'. What are the coordinates of the center of rotation?

This geometry problem involves determining the center of rotation for a 90° clockwise rotation that maps triangle R onto triangle R'. Through geometric reasoning and midpoint analysis, the center of rotation is found to be (4, 4). Suitable for students in Grades 9-11.

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