To map triangle $ABC$ to triangle $A'B'C'$, we need to describe the sequence of transformations. From the image, we can observe the following:

1. Original Points (Triangle ABC):

   • $A(2, -7)$
   • $B(6, -5)$
   • $C(0, 2)$

2. Transformed Points (Triangle A'B'C'):

   • $A'(-4, -1)$
   • $B'(-6, -3)$
   • $C'(-3, 1)$

Sequence of Transformations:

Step 1: Rotation by 90° clockwise

• Rotating triangle ABC by 90° clockwise around the origin will move the points as follows:
  • $A(2, -7) \to A'(-4, -1)$
  • $B(6, -5) \to B'(-6, -3)$
  • $C(0, 2) \to C'(-3, 1)$

This rotation explains the transformation from triangle $ABC$ to triangle $A'B'C'$.

Conclusion:

The transformation that maps triangle $ABC$ onto triangle $A'B'C'$ is a 90° clockwise rotation about the origin.

Would you like further details or have any other questions?

Here are 5 related questions to explore:

1. What are the effects of rotating a shape by different angles (e.g., 180°, 270°)?
2. How does a reflection differ from a rotation in terms of transformations?
3. How can you determine the center of rotation for any given transformation?
4. What are some real-life applications of geometric transformations?
5. What is the difference between clockwise and counterclockwise rotations?

Tip: When rotating a figure, positive angles typically indicate counterclockwise rotation, while negative angles indicate clockwise rotation.