https://file.aiquickdraw.com/mathbot/file/1729552062640bd2409nb.jpg

In the provided image, we have two parallelograms: the preimage (black) and the image (blue). The task is to find the translation rule that maps the preimage to the image.

### Steps to find the translation rule:
1. **Pick any point on the preimage and its corresponding point on the image.**
   Let's take the bottom-left corner of the preimage, located at \((-3, -3)\), and its corresponding point on the image, located at \((1, 4)\).

2. **Find the horizontal and vertical shifts.**
   - Horizontal shift (change in \(x\)): \(1 - (-3) = 1 + 3 = 4\)
   - Vertical shift (change in \(y\)): \(4 - (-3) = 4 + 3 = 7\)

3. **Translation rule:**
   The translation can be expressed as \((x, y) \to (x + 4, y + 7)\).

So, the translation rule is:
\[
(x, y) \to (x + 4, y + 7)
\]

Let me know if you'd like further clarification or if you have any questions! 

### Related Questions:
1. How do you verify that a translation is correct for all points?
2. Can translations be combined with other transformations like reflections or rotations?
3. What happens to the orientation of a shape during translation?
4. How would you describe the transformation if the shape moved diagonally in the opposite direction?
5. Can a translation ever change the size of a shape?

### Tip:
When determining a translation, it's often easiest to work with the corners or distinctive points of a shape for clarity.

Use the graph below to enter a single translation rule. Complete the rule that describes the translation: (x, y) -> ?

Learn how to find the translation rule that maps a parallelogram in a coordinate plane. Understand the shifts in the x and y directions and how to express the translation as an ordered pair. Suitable for students in Grades 7-9.

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