https://file.aiquickdraw.com/mathbot/file/1726264658827d5x3ujii.jpg

Let's analyze the translation between the two shapes, A and B, shown in the grid.

1. **Translation from Shape A to Shape B (a):**
   - The center of **Shape A** is located at coordinates \((-4, 4)\).
   - The center of **Shape B** is located at coordinates \((2, -3)\).
   - To find the vector that describes the translation from A to B, we calculate the difference in the x- and y-coordinates:
     - The x-coordinate changes from \(-4\) to \(2\), so the change in x is: \(2 - (-4) = 6\).
     - The y-coordinate changes from \(4\) to \(-3\), so the change in y is: \(-3 - 4 = -7\).
   - Thus, the translation vector from Shape A to Shape B is \(\mathbf{v} = (6, -7)\).

2. **Translation from Shape B to Shape A (b):**
   - To reverse the translation, we simply take the opposite of the vector from A to B.
   - The vector from Shape B to Shape A is \(\mathbf{v} = (-6, 7)\).

### Summary:
- **a)** The vector from Shape A to Shape B is \(\mathbf{v} = (6, -7)\).
- **b)** The vector from Shape B to Shape A is \(\mathbf{v} = (-6, 7)\).

Would you like further details or explanations?

Here are 5 related questions:
1. How do you determine the coordinates of a point in a Cartesian plane?
2. What is the general formula for finding a translation vector between two points?
3. How do negative and positive vectors affect translations on a coordinate plane?
4. Can you explain how to reverse a translation vector?
5. How would a translation affect the orientation or shape of an object?

**Tip:** When calculating translations, always subtract the starting point from the ending point to get the correct vector.

What vector describes the translation from shape A to shape B and from shape B to shape A?

Learn how to calculate translation vectors between two shapes on a Cartesian plane. This problem involves determining the translation from shape A to shape B, and from shape B to shape A, using coordinate geometry and vector principles. Suitable for students in Grades 8-10.

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