https://file.aiquickdraw.com/mathbot/file/1726143375914jjhf86um.jpg

The problem shows two triangles, \(\triangle ABC\) and \(\triangle A'B'C'\), and asks for the sequence of transformations that maps \(\triangle ABC\) to \(\triangle A'B'C'\). The transformation involves a reflection followed by a translation.

### Analysis of the Reflection:
- The original triangle, \(\triangle ABC\), is positioned in the second quadrant, while \(\triangle A'B'C'\) is positioned in the first quadrant.
- From the reflection choices, we can deduce that a reflection across the **y-axis** is needed because this would move the points from the left side of the y-axis to the right side. 

### Translation:
- After the reflection, the reflected triangle would still be relatively close to the origin, while the triangle \(\triangle A'B'C'\) is further along the positive x-axis.
- To complete the transformation, a translation along the **positive x-axis** is needed to match the position of \(\triangle A'B'C'\).

### Conclusion:
The sequence of transformations that maps \(\triangle ABC\) to \(\triangle A'B'C'\) is:
- **Reflection across the y-axis**, followed by a **translation to the right**.

Let me know if you'd like more details or have any questions!

Here are 5 related questions to deepen your understanding:
1. What happens when you reflect a figure across the x-axis instead of the y-axis?
2. How can you determine the direction and distance of a translation from one triangle to another?
3. Can any triangle be mapped to another triangle using a combination of reflections, rotations, and translations?
4. How does a reflection across the line \( y = x \) differ from one across the y-axis?
5. What types of transformations are considered rigid transformations?

**Tip:** Reflections flip shapes across a specific line, changing their orientation, but translations preserve orientation and move them without flipping.

A sequence of transformations maps ∆ABC to ∆A'B'C'. The sequence of transformations that maps ∆ABC to ∆A'B'C' is a reflection across the ___ followed by a translation ___ .

Explore how to map ∆ABC to ∆A'B'C' using a reflection across the y-axis followed by a translation to the right. This problem focuses on rigid transformations such as reflections and translations in coordinate geometry, suitable for Grades 8-10.

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