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To determine the vector that translates shape E to shape F, we will compare the positions of corresponding points from both shapes.

1. Identify a key point on shape E, such as the bottom-left corner.
   - Coordinates of the bottom-left corner of shape E: (3, 1).

2. Identify the corresponding point on shape F, such as its bottom-left corner.
   - Coordinates of the bottom-left corner of shape F: (8, 5).

3. To find the translation vector, subtract the coordinates of shape E from shape F:
   \[
   (8 - 3, 5 - 1) = (5, 4)
   \]

Thus, the vector that translates shape E to shape F is **(5, 4)**.

Would you like a detailed explanation on vectors or any clarifications?

Here are 5 related questions to extend your understanding:
1. How do you determine the direction of a translation vector?
2. What would the vector be if shape F was moved back to shape E?
3. Can a translation vector ever change the shape or size of an object?
4. How would you find the vector if shape F was rotated instead of translated?
5. How can translation vectors be applied in real-world applications like robotics?

**Tip:** When finding translation vectors, always focus on corresponding points between the shapes, such as corners or specific vertices.

What vector translates shape E to shape F?

Learn how to find the translation vector that moves shape E to shape F on a coordinate grid. This problem involves identifying key points on both shapes, comparing their coordinates, and applying the translation vector formula to find the vector (5, 4). Suitable for Grades 7-9.

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