Question

the triangle fgh is a dilation of the triangle fgh. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Find the length of \(GG'\) and \(GG\)

The \(y -\)coordinate of \(G\) is \(10\) and the \(y -\)coordinate of \(G'\) is \(4\).
The length of \(GG'=4\) (from the graph, vertical side of the smaller triangle), and the length of \(GG = 10\) (vertical side of the larger triangle).

Step2: Calculate the scale factor

The scale factor \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\)
\(k=\frac{4}{10}\)
Simplify \(\frac{4}{10}=\frac{2}{5}\)

Answer:

\(\frac{2}{5}\)