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The problem shows that Jeffrey has translated \( \Delta ABC \) to \( \Delta A'B'C' \), and the graph illustrates the movement. The task is to identify the correct translation rule for this transformation.

### Observations:
- Triangle \( ABC \) is in the first quadrant.
- Triangle \( A'B'C' \) is in the third quadrant, suggesting the triangle was moved left and down.

### Coordinate Analysis:
By examining the movement of the points:
1. **Point A (Initial):** \( A = (0, 0) \)
   - **Point A' (After translation):** \( A' = (-8, -6) \)
   - This means \( A \) was translated by \( -8 \) in the x-direction and \( -6 \) in the y-direction.

2. **Point B (Initial):** \( B = (0, 5) \)
   - **Point B' (After translation):** \( B' = (-8, -1) \)
   - This confirms the same translation by \( -8 \) in the x-direction and \( -6 \) in the y-direction.

3. **Point C (Initial):** \( C = (4, 0) \)
   - **Point C' (After translation):** \( C' = (-4, -6) \)
   - Again, the translation is \( -8 \) in the x-direction and \( -6 \) in the y-direction.

### Translation Rule:
The translation of the triangle can be described as:
\[
(x, y) \rightarrow (x - 8, y - 6)
\]

This rule applies to all the points of the triangle, shifting it uniformly.

Would you like more details on this? Here are a few related questions you can explore:

1. How do you determine a translation from a graph?
2. What are the differences between translations, reflections, and rotations in geometry?
3. What other transformations could result in similar-looking figures?
4. How would the coordinates change if the triangle were reflected instead of translated?
5. How do you compose multiple transformations, such as translation followed by a rotation?

**Tip:** When solving transformation problems, focus on one point first to determine the shift, and then verify it with the other points!

Jeffrey translated ΔABC to get to ΔA'B'C'. Which of the following coordinate notations will describe Jeffrey's transformation of the triangle?

Learn how Jeffrey translated triangle ΔABC to ΔA'B'C' by applying the translation rule (x, y) → (x - 8, y - 6). This problem covers key geometry concepts related to transformations on a coordinate plane, suitable for Grades 9-10.

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