https://file.aiquickdraw.com/mathbot/file/1729792557886wmxiy8e6.jpg

The question asks for the rigid motion that maps \( \triangle DEF \) onto \( \triangle ABC \). From the image, we can observe the following coordinates:

- \( \triangle DEF \):
  - \( D(-5, -5) \)
  - \( E(-5, -3) \)
  - \( F(-3, -5) \)

- \( \triangle ABC \):
  - \( A(0, 0) \)
  - \( B(2, 0) \)
  - \( C(0, 2) \)

One way to map these triangles is through a combination of transformations. A common type of rigid motion could be a reflection followed by a translation or rotation.

Upon examining, a reflection across the line \( y = x \) would map \( \triangle DEF \) to the same orientation as \( \triangle ABC \).

Thus, the correct rigid motion is likely:
- **Reflection over \( y = x \)**.

Would you like more details on the steps or reasoning? Here are some follow-up questions to consider:

1. How do you identify if two triangles are congruent under a rigid motion?
2. What is the significance of reflection in rigid motion transformations?
3. Could a rotation also map \( \triangle DEF \) onto \( \triangle ABC \)? Why or why not?
4. How do you determine the line of reflection when mapping two triangles?
5. Are there other transformations that could also achieve this mapping?

**Tip:** Always check the orientation of the shapes when performing rigid motions to ensure you’re applying the correct transformation.

What rigid motion maps triangle DEF onto triangle ABC?

This problem involves mapping triangle DEF onto triangle ABC using a rigid motion. It explores the concept of reflection over the line y=x and determining congruence through rigid transformations. Suitable for students in Grades 8-10.

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