https://file.aiquickdraw.com/mathbot/file/172840002137221wglzl5.jpg


Write a rule describing each translation below.

The image shows a transformation of a triangle \( \triangle PQR \) to \( \triangle P'Q'R' \). To find the rule of translation, we need to determine how each point of the triangle is shifted from its original position to its new position.

### Step-by-Step Analysis:
1. **Identify the Coordinates:**
   - **Original Triangle:**
     - \( P \): (2, 5)
     - \( Q \): (4, 7)
     - \( R \): (0, 3)

   - **Transformed Triangle:**
     - \( P' \): (2, -3)
     - \( Q' \): (4, -1)
     - \( R' \): (0, -5)

2. **Determine the Translation:**
   - Let's calculate the change in \( x \)- and \( y \)-coordinates from each point of \( \triangle PQR \) to \( \triangle P'Q'R' \).

   - \( P \) to \( P' \):
     - \( x \)-change: \( 2 - 2 = 0 \)
     - \( y \)-change: \( -3 - 5 = -8 \)

   - \( Q \) to \( Q' \):
     - \( x \)-change: \( 4 - 4 = 0 \)
     - \( y \)-change: \( -1 - 7 = -8 \)

   - \( R \) to \( R' \):
     - \( x \)-change: \( 0 - 0 = 0 \)
     - \( y \)-change: \( -5 - 3 = -8 \)

3. **Translation Rule:**
   Each point is shifted **8 units down**. Thus, the translation rule can be described as:
   \[
   (x, y) \rightarrow (x, y - 8)
   \]

Would you like to go through any more details or have questions about this translation?

### Related Questions:
1. How would the translation change if the transformation moved the triangle 5 units to the right instead?
2. What would be the coordinates of \( \triangle P'Q'R' \) if the translation were \( (x, y) \rightarrow (x + 3, y - 8) \)?
3. How does reflecting the triangle over the x-axis affect the coordinates of \( \triangle PQR \)?
4. What is the formula for a general translation in the coordinate plane?
5. Can you find the midpoint between \( P \) and \( P' \) in this translation?

### Tip:
When working with translations, always subtract the original coordinates from the new ones to find the exact change in the \( x \)- and \( y \)-directions.

Write a rule describing each translation below.

Understand how to find the rule of translation for a triangle on a coordinate plane. This problem involves translating points from one position to another using the translation formula. Suitable for students in Grades 6-8.

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