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.