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To determine the translation that maps \(\triangle ABC\) (the blue triangle) to \(\triangle A'B'C'\) (the pink triangle), we can compare the coordinates of corresponding points on the two triangles.

### Step 1: Identify the Coordinates of the Points
- **\(A\)** is at \((-1, 2)\)
- **\(B\)** is at \((2, 5)\)
- **\(C\)** is at \((1, 1)\)

- **\(A'\)** is at \((3, 6)\)
- **\(B'\)** is at \((6, 9)\)
- **\(C'\)** is at \((5, 5)\)

### Step 2: Calculate the Translation
The translation vector \((x, y)\) can be found by subtracting the coordinates of each point \(A\), \(B\), and \(C\) from the corresponding points \(A'\), \(B'\), and \(C'\).

- From \(A\) to \(A'\): 
  \[
  x\text{-translation} = 3 - (-1) = 4, \quad y\text{-translation} = 6 - 2 = 4
  \]
  
- From \(B\) to \(B'\):
  \[
  x\text{-translation} = 6 - 2 = 4, \quad y\text{-translation} = 9 - 5 = 4
  \]
  
- From \(C\) to \(C'\):
  \[
  x\text{-translation} = 5 - 1 = 4, \quad y\text{-translation} = 5 - 1 = 4
  \]

### Conclusion:
The translation that maps \(\triangle ABC\) to \(\triangle A'B'C'\) is a shift **4 units to the right** and **4 units up**.

Would you like more details or have any questions? Here are some additional questions related to this topic:

1. How do you determine the translation vector if given only the coordinates of the initial and final points?
2. What is the effect of a translation on the size and shape of a geometric figure?
3. How would you describe a reflection or rotation, instead of a translation?
4. Can the translation be represented using matrix operations? How?
5. How would the process change if the translation used negative values?

**Tip:** When working with translations on a graph, always check corresponding points to confirm the consistency of the translation across all points.

Determine the translation that maps ΔABC (blue triangle) to ΔA'B'C' (pink triangle) on the coordinate plane. Use non-negative numbers.

Learn how to determine the translation that maps one triangle to another on a coordinate plane. This problem involves understanding translations and using the translation formula. Suitable for students in Grades 6-8.

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