Question

the triangle uvw is a dilation of the triangle uvw. 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 corresponding sides

Let's consider the \(y -\)coordinates of \(V\) and \(V'\). The \(y -\)coordinate of \(V\) is \(- 10\) and the \(y -\)coordinate of \(V'\) is \(-2\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\).
If we consider the vertical distance from the \(x -\)axis (since \(U\) and \(U'\) are on the \(x -\)axis), for the points \(V\) and \(V'\), \(k=\frac{|- 2|}{|-10|}\)

$$k = \frac{2}{10}=\frac{1}{5}$$

Answer:

\(\frac{1}{5}\)