Question

what is the scale factor of the dilation of triangle def?
$\frac{3}{10}$
$\frac{3}{7}$
$\frac{7}{3}$
7

Explanation:

Step1: Recall the formula for scale factor

The scale factor of a dilation is the ratio of the length of a side of the image to the length of the corresponding side of the original figure.

Step2: Identify the corresponding sides

In this case, for the dilation of triangle \(DEF\) to triangle \(D'E'F'\), if we consider the sides from the center of dilation \(O\) to the vertices. Let's assume the side \(OF'\) (image side) has length \(3\) and the side \(OF\) (original side) has length \(7\).

Step3: Calculate the scale factor

The scale factor \(k=\frac{\text{length of image side}}{\text{length of original side}}\). So \(k = \frac{OF'}{OF}=\frac{3}{7}\)

Answer:

$\frac{3}{7}$