Question

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

Explanation:

Step1: Find length of side in original and dilated parallelogram

Let's assume we find the length of a side. For example, if we consider the horizontal - like side. In parallelogram \(FGHJ\), assume the length of a side (by counting grid units) is \(2\) units. In parallelogram \(F'G'H'J'\), the length of the corresponding side (by counting grid units) is \(8\) units.

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\). But since \(FGHJ\) is the pre - image and \(F'G'H'J'\) is the image (after dilation and translation, translation does not affect the size), if we use the formula \(k = \frac{\text{length of side in pre - image}}{\text{length of side in image}}\) (because \(FGHJ\) is dilated to get \(F'G'H'J'\), we can also think in terms of similarity ratio. If \(a\) is the side of \(FGHJ\) and \(A\) is the side of \(F'G'H'J'\), \(k=\frac{a}{A}\)). Let \(a = 2\) (side of \(FGHJ\)) and \(A=8\) (side of \(F'G'H'J'\)), then \(k=\frac{2}{8}=\frac{1}{4}\)

Answer:

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