https://file.aiquickdraw.com/mathbot/file/17255955317413sn3gpzh.jpg

The image shows two triangles, \( \triangle ABCD \) (in blue) and \( \triangle A'B'C'D' \) (in yellow), on a coordinate plane, with instructions to write the translation rule.

### Steps to Determine the Translation Rule:

1. Identify corresponding points between the triangles \( \triangle ABCD \) and \( \triangle A'B'C'D' \):
   - Find the coordinates of points in \( \triangle ABCD \) (blue) and their corresponding points in \( \triangle A'B'C'D' \) (yellow).

2. Calculate the translation (the change in \( x \) and \( y \)) by comparing the coordinates of corresponding points.

For example:
- Let’s use point \( A \) from \( \triangle ABCD \) and point \( A' \) from \( \triangle A'B'C'D' \).
- Suppose \( A \) has coordinates \( (x_A, y_A) \) and \( A' \) has coordinates \( (x_{A'}, y_{A'}) \).

3. Use the following translation formula:
   \[
   (x, y) \to (x + \Delta x, y + \Delta y)
   \]
   where \( \Delta x = x_{A'} - x_A \) and \( \Delta y = y_{A'} - y_A \).

### Analyzing from Image:
- I'll need to estimate the coordinates of the points. From the image, it appears that \( A \), \( B \), \( C \), and \( D \) correspond to the respective points \( A' \), \( B' \), \( C' \), and \( D' \).

Let me check those coordinates and work out the translation.The translation rule for the triangles is:

\[
(x, y) \to (x - 4, y + 4)
\]

This means that to translate \( \triangle ABCD \) to \( \triangle A'B'C'D' \), you move each point 4 units to the left and 4 units up.

Would you like further details or have any questions? Here are some related questions to explore:

1. How would the translation rule change if you shifted the triangle 5 units down instead?
2. What is the effect of translating a shape on its size and orientation?
3. How would you reflect \( \triangle ABCD \) across the y-axis instead of translating it?
4. Could you combine a translation with a rotation? What would the rule look like?
5. What if you wanted to scale \( \triangle ABCD \) along with translating it?

**Tip:** Translations always preserve the shape and size of geometric figures—they only change the position on the coordinate plane.

△A'B'C'D' is a translation of △ABCD. Write the translation rule.

Learn how to find the translation rule for △A'B'C'D', a transformation of △ABCD on the coordinate plane. The problem explores key concepts of coordinate geometry and translations. Suitable for students in Grades 7-9.

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