https://file.aiquickdraw.com/mathbot/file/1731468385388beir7fw6.jpg

To find the coordinates of the point \( A' \) after translating the point \( A(-4, 3) \) by the vector \( \langle 5, -1 \rangle \), you can use the following steps:

1. **Identify the original coordinates of \( A \):**
   \[ A = (-4, 3) \]

2. **Identify the components of the translation vector \( \langle 5, -1 \rangle \):**
   \[ \text{Vector} = (5, -1) \]

3. **Apply the translation by adding each component of the vector to the corresponding coordinate of \( A \):**
   \[ A'_x = -4 + 5 = 1 \]
   \[ A'_y = 3 + (-1) = 2 \]

4. **Thus, the coordinates of \( A' \) are:**
   \[ A' = (1, 2) \]

### Answer:
The coordinates of \( A' \) are \( (1, 2) \).

Would you like further explanation on this solution, or do you have any additional questions?

Here are some related questions that could expand on this information:

1. How do you determine the translation vector for different transformations?
2. What would be the coordinates of \( A' \) if the vector were \( \langle -5, 1 \rangle \) instead?
3. How would this solution change if we were performing a reflection instead of a translation?
4. What is the general rule for translating a point \( (x, y) \) by a vector \( \langle a, b \rangle \)?
5. How would you graph the original and translated points on a coordinate plane?

**Tip:** When translating points, add the components of the vector to the corresponding coordinates of the point to get the new position easily.

The point A(-4, 3) is translated along the vector <5, -1>. The image is A'. Find the coordinates of A'.

Learn how to find the coordinates of point A' by translating point A(-4, 3) along the vector <5, -1>. This problem covers essential concepts in coordinate geometry and translation of points. Suitable for students in Grades 6-8.

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