From the image, I can deduce the transformation involves a translation and a dilation of triangle $\triangle XYZ$ to $\triangle X'Y'Z'$. The task is to find the scale factor of the dilation by comparing the sizes of corresponding sides of $\triangle XYZ$ and $\triangle X'Y'Z'$.

Steps to find the scale factor:

1. Locate a corresponding pair of sides: For example, the side between $X$ and $Y$ in $\triangle XYZ$ and between $X'$ and $Y'$ in $\triangle X'Y'Z'$.

2. Measure or calculate the lengths of these sides.

   • The side $XY$ (on the larger blue triangle) has a length of approximately 15 units (from point $X$ at $(-10, 0)$ to point $Y$ at $(5, 0)$).
   • The side $X'Y'$ (on the smaller yellow triangle) has a length of 3 units (from point $X'$ at $(-5, 6)$ to point $Y'$ at $(0, 6)$).

3. Calculate the scale factor: $\text{Scale factor} = \frac{\text{Length of } X'Y'}{\text{Length of } XY} = \frac{3}{15} = \frac{1}{5}$

Thus, the scale factor for the dilation is $\frac{1}{5}$.

Summary:

• The scale factor of the dilation is $\frac{1}{5}$.

Would you like further details on how the translation works, or do you have any questions?

Here are 5 related questions to expand on this concept:

1. What is the general formula for finding the scale factor in a dilation?
2. How does translation affect the coordinates of points in a triangle?
3. Can a dilation have a scale factor larger than 1? What does that imply?
4. How would you reverse a dilation with a scale factor of $\frac{1}{5}$?
5. How is the center of dilation determined in these transformations?

Tip: When dealing with dilations, always ensure to compare corresponding sides or distances from the center of dilation to maintain accuracy.