https://file.aiquickdraw.com/mathbot/file/1730401160349urumqbo0.jpg

To determine the sequence of rigid motions that maps figure \(ABCD\) onto figure \(PQRS\), let's analyze the transformations step by step.

1. **Rotation or Reflection Analysis:**
   - Observing \(ABCD\) and \(PQRS\), \(PQRS\) appears to be rotated relative to \(ABCD\) around the origin.
   - If we rotate \(ABCD\) by 90° counterclockwise around the origin, we can approximate \(PQRS\)'s orientation.
   
2. **Translation Check:**
   - After a 90° counterclockwise rotation, \(ABCD\) would map closely to \(PQRS\) in terms of shape and orientation. However, there is a shift: \(PQRS\) is slightly below the rotated image of \(ABCD\).
   - Therefore, a final translation downwards is needed.

3. **Answer Conclusion:**
   - Based on the options provided and our observations, the correct sequence of rigid motions should be:
     - **90° counterclockwise rotation around the origin**, followed by a **translation 2 units down**.

Thus, the correct answer is:
- **90° counterclockwise rotation around the origin followed by a translation 2 units down**.

Would you like more details on each transformation? 

### Related Questions:
1. How do we determine the rotation angle needed for two shapes to align?
2. What are rigid motions, and why do they preserve the shape and size of figures?
3. How can we determine if a figure requires a translation after rotation?
4. What is the difference between clockwise and counterclockwise rotations?
5. How do reflections across axes affect the orientation of figures?

### Tip:
When working with transformations, it helps to apply each transformation step-by-step on grid paper to visualize the result clearly.

Which sequence of rigid motions maps figure ABCD onto figure PQRS in the given diagram?

Understand how to map figure ABCD onto figure PQRS using rigid motions. This problem involves a sequence of transformations, including a 90° counterclockwise rotation around the origin followed by a translation 2 units down. Ideal for students in Grades 8-10 exploring geometry and transformations.

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