Question

find the scale factor used for the dilation between the similar figures. abcd ~ fghe

Explanation:

Step1: Determine the lengths of corresponding sides

Let's assume the side length of the larger square \(ABCD\) is \(4\) units (counting the grid - squares) and the side length of the smaller square \(FGHE\) is \(2\) units.

Step2: Calculate the scale factor

The scale factor \(k\) is given by the ratio of the side lengths of the similar figures. If \(s_1\) is the side length of the larger figure and \(s_2\) is the side length of the smaller figure, then \(k=\frac{s_2}{s_1}\). Substituting \(s_1 = 4\) and \(s_2=2\), we get \(k = \frac{2}{4}=\frac{1}{2}\)

Answer:

\(\frac{1}{2}\)