Question

triangle abc was dilated and translated to form similar triangle abc. what is the scale factor of the dilation?
$\frac{1}{5}$
$\frac{2}{5}$
$\frac{5}{2}$
$\frac{5}{1}$

Explanation:

Step1: Find the length of corresponding sides

In triangle \(ABC\), assume \(BC\) is one side. From the graph, \(BC = 2\) units. In triangle \(A'B'C'\), the corresponding side \(B'C'= 5\) units.

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\). So \(k = \frac{B'C'}{BC}\). Substituting the values, we get \(k=\frac{5}{2}\)

Answer:

\(\frac{5}{2}\) (the third option)