Question

plane geometry
hw: lesson 3 - 3
due fri 10/31
*not accepted after the unit 3 test #1
name: pg 2
4.) pentagon abcde is dilated to get pentagon abcde using center f. what is the scale factor of this dilation? show your calculation.

Explanation:

Step1: Identify corresponding sides

The original pentagon \(ABCDE\) and the dilated pentagon \(A'B'C'D'E'\). Let's take side \(AB = 3\) and \(A'B'=5\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. So, \(k=\frac{\text{length of side in dilated figure}}{\text{length of corresponding side in original figure}}\). Using \(AB = 3\) and \(A'B' = 5\), we have \(k=\frac{5}{3}\approx1.67\).

Answer:

The scale factor of the dilation is \(\frac{5}{3}\)