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To determine the scale factor of the dilation between the triangles \( \triangle ABC \) and \( \triangle A'B'C' \), we need to compare the corresponding side lengths of the two triangles.

### Step-by-step:

1. **Choose Corresponding Sides**: 
   - The triangle \( \triangle ABC \) is the original figure (in blue), and \( \triangle A'B'C' \) is the dilated image (in pink).
   - One straightforward approach is to select corresponding sides, for example, \( \overline{AB} \) and \( \overline{A'B'} \).

2. **Measure the Side Lengths**:
   - Count the number of grid units for side \( AB \) and side \( A'B' \).
     - \( AB \) appears to be 2 units long.
     - \( A'B' \) appears to be 4 units long.

3. **Calculate the Scale Factor**:
   The scale factor is the ratio of the side length of the image to the side length of the original triangle. Therefore, the scale factor \( k \) is:
   \[
   k = \frac{\text{length of } A'B'}{\text{length of } AB} = \frac{4}{2} = 2
   \]

Thus, the scale factor of the dilation is **2**.

Would you like further clarification or additional details?

### 5 Related Questions:
1. How do you find the scale factor for other sides of the triangle?
2. What happens to the area of a shape after a dilation with scale factor 2?
3. How does a dilation affect the angles of a triangle?
4. Can you dilate a triangle with a scale factor less than 1? What happens?
5. What is the center of dilation, and how is it determined?

### Tip:
Always check multiple corresponding sides when calculating a scale factor to ensure accuracy.

What is the scale factor of the dilation between triangle ABC and its dilated image A'B'C'?

Learn how to determine the scale factor of a dilation for triangle ABC and its image A'B'C'. By comparing corresponding sides, the scale factor is calculated using simple geometry concepts. Suitable for students in Grades 7-9.

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