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 \(k\) of a dilation is given by \(k=\frac{\text{length of a side in the image}}{\text{length of the corresponding side in the pre - image}}\). Here, we consider the sides \(OF'\) and \(OF\). The side \(OF' = 3\) (length of the side in the image \(\triangle D'E'F'\)) and \(OF = 7\) (length of the corresponding side in the pre - image \(\triangle DEF\)).

Step2: Calculate the scale factor

The scale factor \(k=\frac{OF'}{OF}\). Substituting the values \(OF' = 3\) and \(OF = 7\) into the formula, we get \(k=\frac{3}{7}\).

Answer:

\(\frac{3}{7}\)