Question

the triangle abc is a dilation of the triangle abc. what is the scale factor of the dilation?

Explanation:

Step1: Identify corresponding side lengths

Let's consider the vertical side - length of $\triangle ABC$ from $C$ to $A$ and the vertical side - length of $\triangle A'B'C'$ from $C'$ to $A'$. The length of the vertical side of $\triangle ABC$ from $C(- 6,-6)$ to $A(-6,-10)$ is $|-6-(-10)| = 4$. The length of the vertical side of $\triangle A'B'C'$ from $C'(-1,-1)$ to $A'(-1,-2)$ is $|-1-(-2)| = 1$.

Step2: Calculate the scale factor

The scale factor $k$ of a dilation is given by the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. So, $k=\frac{\text{length of side in }\triangle A'B'C'}{\text{length of corresponding side in }\triangle ABC}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$