Question

parallelogram fghi was dilated and translated to form similar parallelogram fghj. what is the scale factor of the dilation? 8 4 1/4 1/8

Explanation:

Step1: Determine corresponding side lengths

Let's assume the length of a side in the larger parallelogram \(FGHJ\) is \(8\) units (by counting the grid - squares along a side), and the length of the corresponding side in the smaller parallelogram \(FG'H'J'\) is \(2\) units.

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of a side in the image}}{\text{length of the corresponding side in the pre - image}}\). Here, if we consider the pre - image as \(FGHJ\) and the image as \(FG'H'J'\), then \(k = \frac{2}{8}=\frac{1}{4}\).

Answer:

\(\frac{1}{4}\)