Question

the trapezoid bcde is a dilation of the trapezoid bcde. 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: Select corresponding sides

Choose the vertical sides \(BB'\) and \(BC\). \(B=(0, 2)\), \(B'=(0, 10)\), \(C=(2, 2)\). The length of \(BC = 2\), and the length of \(BB'=10 - 2=8\).

Step2: Calculate scale - factor

The scale factor \(k\) of a dilation is given by the ratio of the length of the corresponding side of the image to the length of the corresponding side of the pre - image. So \(k=\frac{BB'}{BC}\). Substituting the values, we get \(k = \frac{8}{2}=4\).

Answer:

4