I see you've uploaded an image. I'll examine the content to assist you with the math problem shown in the image.

Analyzing the Image:

The image contains two triangles on a coordinate grid, labeled with points $A$, $B$, and $C$ for the left triangle, and points $A'$, $B'$, and $C'$ for the right triangle. The triangles are part of a problem asking about geometric transformations.

Problem Statement:

• The task asks you to describe a transformation that maps triangle $ABC$ onto triangle $A'B'C'$.

Solution:

From the image, we can see that triangle $ABC$ has been reflected over a vertical line. To determine the exact transformation:

1. Locate Points:

   • The coordinates of the points of triangle $ABC$ and triangle $A'B'C'$ need to be identified. Without clear coordinates from the image, it appears that triangle $ABC$ and $A'B'C'$ are symmetric about the vertical axis (which seems to be passing through $x = 2$).

2. Reflection:

   • The transformation is a reflection across the vertical line $x = 2$. This line is the perpendicular bisector of the segments connecting corresponding points from $ABC$ to $A'B'C'$.

Conclusion: The transformation that maps triangle $ABC$ onto triangle $A'B'C'$ is a reflection across the vertical line $x = 2$.

Do you want any further details on this transformation or have any other questions?

Here are some related questions to consider:

1. How do you identify the line of reflection in a geometric transformation?
2. What are other types of transformations that could map triangle $ABC$ onto triangle $A'B'C'$?
3. How do you verify a transformation on a coordinate plane?
4. What is the effect of a reflection on the coordinates of a point?
5. Can a combination of transformations map triangle $ABC$ onto triangle $A'B'C'$?

Tip: Always double-check your line of reflection by verifying that it is equidistant from corresponding points in the original and transformed figures.