https://file.aiquickdraw.com/mathbot/file/17300013565998fzspcug.jpg

To determine the algebraic rule that represents the transformation shown on the grid, let's analyze the movement of each point:

1. **Identify Points in the Original and Transformed Figures:**
   - In the original figure, points are labeled \( A \), \( B \), \( C \), \( D \), and \( E \).
   - In the transformed figure, these points are labeled as \( A' \), \( B' \), \( C' \), \( D' \), and \( E' \).

2. **Examine the Transformation:**
   - Observing the coordinates of each original point and comparing it to its corresponding transformed point, we can see that the triangle has moved downward.
   - Specifically, each point has shifted down by 3 units.

3. **Algebraic Rule for the Transformation:**
   - Since each point is moved down by 3 units, this is a vertical translation.
   - The rule for this transformation is:  
     \[
     (x, y) \rightarrow (x, y - 3)
     \]

### Conclusion:
The algebraic rule that represents the transformation shown on the grid is:
\[
(x, y) \rightarrow (x, y - 3)
\]

Would you like more details or have any questions?

### Related Questions:
1. What happens if we apply the transformation \( (x, y) \rightarrow (x, y + 3) \)?
2. How can we describe transformations that involve rotations?
3. What is the difference between translations and reflections in terms of algebraic rules?
4. How would this transformation look if it was applied in the opposite direction?
5. How do transformations affect the size and shape of geometric figures?

### Tip:
When identifying transformations, it helps to carefully examine how each point moves in relation to its original position.

Which algebraic rule represents the transformation shown on the grid?

Explore how to identify the algebraic rule representing a transformation on a coordinate grid. This problem focuses on understanding translation rules, specifically moving points downward by 3 units. Suitable for students in Grades 6-8.

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