Certainly! Let's break down and solve the problem step by step.
### Part A: Translation Description
The translation given is according to the rule (x, y) → (x - 3, y + 4). This translation can be described in words as follows:
- Move each point 3 units to the left.
- Move each point 4 units up.
### Part B: Calculating New Coordinates
Next, we need to determine the new coordinates of the vertices A', B', and C' after applying the translation.
The original coordinates of the vertices are:
- A: (-3, 1)
- B: (-3, 4)
- C: (-7, 1)
#### Applying the Translation to Each Vertex:
1. Vertex A(-3, 1):
- New x-coordinate: -3 - 3 = -6
- New y-coordinate: 1 + 4 = 5
- Therefore, A' is at (-6, 5).
2. Vertex B(-3, 4):
- New x-coordinate: -3 - 3 = -6
- New y-coordinate: 4 + 4 = 8
- Therefore, B' is at (-6, 8).
3. Vertex C(-7, 1):
- New x-coordinate: -7 - 3 = -10
- New y-coordinate: 1 + 4 = 5
- Therefore, C' is at (-10, 5).
### Final Coordinates for AA'B'C':
- A' is at (-6, 5)
- B' is at (-6, 8)
- C' is at (-10, 5)
So, the vertices of the translated triangle A'B'C' are located at (-6, 5), (-6, 8), and (-10, 5).