QuestionLesson 3 Practice Problems (1.) Pentagon $A^{\prime} B^{\prime} C^{\prime} D^{\prime} E^{\prime}$ is the image of pentagon $A B C D E$ after a dilation centered at $F$. What is the scale factor of this dilation?

Studdy Solution
Calculate the scale factor using the ratio of corresponding distances. Use either pair of corresponding distances:
$\text{Scale Factor} = \frac{\text{Distance from } F \text{ to a vertex of } A'B'C'D'E'}{\text{Distance from } F \text{ to the corresponding vertex of } ABCDE}$
Using the distances $5$ and $3$:
$\text{Scale Factor} = \frac{5}{3}$
Or using the distances $10$ and $6$:
$\text{Scale Factor} = \frac{10}{6} = \frac{5}{3}$
The scale factor of the dilation is:
$$\boxed{\frac{5}{3}}$$