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.