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To find the vector that translates point \( A \) to \( A' \), we need to determine the difference in coordinates between these two points.

1. From the graph:
   - The coordinates of point \( A \) are \( (-1, 6) \).
   - The coordinates of point \( A' \) are \( (5, 9) \).

2. The translation vector is the difference between the coordinates of \( A' \) and \( A \):
   \[
   \text{Vector} = A' - A = (5 - (-1), 9 - 6) = (6, 3).
   \]

Thus, the vector that translates point \( A \) to point \( A' \) is \( \mathbf{v} = (6, 3) \).

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. What vector translates point \( B \) onto point \( B' \)?
2. What vector translates point \( C \) onto point \( C' \)?
3. How would the translation affect the coordinates of any arbitrary point \( P(x, y) \)?
4. Can you write the transformation matrix for this translation?
5. What is the general formula for finding a translation vector?

**Tip**: When dealing with translations, always subtract the coordinates of the original point from the coordinates of the new point to find the vector.

What vector translates point A onto point A'?

Find the vector that translates point A (-1, 6) to point A' (5, 9). This problem covers key coordinate geometry concepts, including vector translation and graphical transformations. Suitable for students in Grades 7-9.

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