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To determine the composition of transformations that map the rectangle \( ABCD \) to \( A'B'C'D' \), we need to analyze the steps provided:

1. **Rotation**: The first transformation mentioned is a clockwise rotation about the origin. Based on the positions of \( ABCD \) and \( A'B'C'D' \), it seems that the figure has been rotated 90° clockwise. In general, a 90° clockwise rotation about the origin transforms the coordinates \( (x, y) \) to \( (y, -x) \).

   Let’s check:
   - \( A(-5, 6) \rightarrow A'(6, -5) \)
   - \( B(-3, 6) \rightarrow B'(6, -3) \)
   - \( C(-3, 2) \rightarrow C'(2, -3) \)
   - \( D(-5, 2) \rightarrow D'(2, -5) \)

   All points confirm a 90° clockwise rotation.

2. **Reflection**: The second transformation is a reflection. After the 90° rotation, the figure is reflected over the **x-axis**, because the signs of the y-coordinates in the final positions of \( A'B'C'D' \) are opposite to those in the rotated version.

Thus, the composition of transformations is:

- Rotate 90° clockwise about the origin.
- Reflect over the x-axis.

Would you like a more detailed breakdown or further clarification?

Here are 5 related questions you can explore:

1. What are the rules for other common rotations (e.g., 180°, 270°) about the origin?
2. How would the transformation change if reflected over the y-axis instead of the x-axis?
3. What are the formulas for reflections over other lines, like \( y = x \) or \( y = -x \)?
4. How does the order of transformations (e.g., reflecting first, then rotating) affect the result?
5. How would you find the image of a point under a combination of dilation and rotation?

**Tip**: Always apply transformations step-by-step, checking each point to ensure accuracy in composite transformations.

Find the composition of transformations that map ABCD to A'B'C'D'. The instructions provided indicate: 'Rotate clockwise about the origin [ ? ]°, then reflect over the [  ]-axis.'

Analyze the composition of transformations required to map rectangle ABCD to A'B'C'D'. Understand the steps involving a 90° clockwise rotation about the origin, followed by a reflection over the x-axis. Suitable for students in Grades 8-10 studying transformations and coordinate geometry.

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