Question

the parallelogram ( ghij ) is a dilation of the parallelogram ( ghij ). what is the scale factor of the dilation?

Explanation:

Step1: Find the length of a side of the original parallelogram

The length of \(HI\) in parallelogram \(GHIJ\): \(HI = 10-(- 6)=16\) (using the distance formula on the \(x -\)axis: \(x_2 - x_1\), where \(x_2 = 10\), \(x_1=-6\))

Step2: Find the length of the corresponding side of the dilated parallelogram

The length of \(H'I'\) in parallelogram \(G'H'I'J'\): \(H'I'=2 - (-2)=4\) (using the distance formula on the \(x -\)axis: \(x_2 - x_1\), where \(x_2 = 2\), \(x_1=-2\))

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\). So \(k=\frac{H'I'}{HI}=\frac{4}{16}=\frac{1}{4}\)

Answer:

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