Question

the triangle ( lmn ) is a dilation of the triangle ( lmn ). 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: Identify corresponding side lengths

From the graph, the length of \( LN\) (original triangle) is \(1\) unit (since \(L\) is at \((-1,1)\) and \(N\) is at \((0,1)\)), and the length of \(L'N'\) (dilated triangle) is \(3\) units (since \(L'\) is at \((-4,4)\) and \(N'\) is at \((0,4)\)).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of corresponding side in pre - image}}\). So, \(k = \frac{L'N'}{LN}=\frac{3}{1}=3\).

Answer:

\(3\)