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To determine the translation rule for \( R'S' \) as a translation of \( RS \), we need to compare the coordinates of points \( R \), \( S \), \( R' \), and \( S' \).

### Step 1: Identify the coordinates
- Point \( R \) is at \( (-4, -4) \).
- Point \( S \) is at \( (0, -6) \).
- Point \( R' \) is at \( (2, 6) \).
- Point \( S' \) is at \( (6, 4) \).

### Step 2: Calculate the translation
To find the translation rule, subtract the coordinates of the original points \( R \) and \( S \) from their corresponding translated points \( R' \) and \( S' \).

- From \( R \) to \( R' \):
  \[
  (2 - (-4), 6 - (-4)) = (2 + 4, 6 + 4) = (6, 10)
  \]
- From \( S \) to \( S' \):
  \[
  (6 - 0, 4 - (-6)) = (6, 4 + 6) = (6, 10)
  \]

Both points are translated by \( (6, 10) \).

### Step 3: Write the translation rule
The translation rule is:
\[
(x, y) \to (x + 6, y + 10)
\]

Would you like more details or further clarification?

### Related Questions:
1. What is a translation in geometry?
2. How do you apply a translation rule to any point?
3. What other types of transformations exist in geometry?
4. Can translations change the size or orientation of a shape?
5. How would the translation look for other shapes, such as triangles?

### Tip:
When applying translations, always check both \( x \)- and \( y \)-coordinates to ensure consistency across all points in the figure.

R'S' is a translation of RS. Write the translation rule.

Learn how to find the translation rule for a transformation in coordinate geometry, specifically translating RS to R'S'. This example demonstrates how to calculate translations on the coordinate plane, using the points (-4, -4), (0, -6), (2, 6), and (6, 4). Suitable for students in grades 8-10.

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