Question

triangle tuv was dilated to create triangle tuv using point a as the center of dilation. what is the scale factor of the dilation? 2/5 2/3 3/2 8/5

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of a side in the image}}{\text{length of the corresponding side in the pre - image}}\).

Step2: Identify the corresponding sides

Let's consider the sides \(AV'\) and \(AV\). We know that \(AV' = 3.2\) and \(AV=3.2 + 4.8=8\).

Step3: Calculate the scale factor

Using the formula \(k=\frac{AV'}{AV}\), substitute the values: \(k=\frac{3.2}{8}\). Simplify \(\frac{3.2}{8}=\frac{3.2\times10}{8\times10}=\frac{32}{80}=\frac{2}{5}\).

Answer:

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