Short Answer 
The transformation process involves moving points through four main types: rotation, reflection, translation, and dilation. For triangle ABC, the vertices were first reflected across the line y = x, resulting in A’, B’, and C’, and then translated upward by 6 units to achieve the final positions of the vertices.
Step 1: Understand Transformation
The concept of transformation involves moving a point from its original position to a new one. It is crucial to identify the type of transformation being applied, as this will determine how the points change. There are four main types of transformations:
- Rotation – turning around a point.
- Reflection – flipping over a line.
- Translation – sliding to a new location.
- Dilation – resizing an object.
Step 2: Reflect Triangle ABC
For triangle ABC, with vertices at A(-1, 1), B(-3, 5), and C(-6, 5), we begin by applying a reflection across the line y = x. This means that the x- and y-coordinates of each vertex will be swapped:
- A’ becomes (1, -1).
- B’ becomes (5, -3).
- C’ becomes (5, -6).
Step 3: Translate Triangle A’B’C’
After the reflection, the next step is to translate the new triangle A’B’C’ up by 6 units. This means adding 6 to the y-coordinate of each vertex from after the reflection:
- A’ moves to (1, 5).
- B’ moves to (5, 3).
- C’ moves to (5, 0).