Question

the parallelogram qrst is a dilation of the parallelogram qrst. what is the scale factor of the dilation?

Explanation:

Step1: Identify corresponding side lengths

In a dilation, the scale factor \(k\) is the ratio of a side length of the image to the corresponding side length of the pre - image. Let's consider the horizontal sides. For parallelogram \(QRST\), if we assume \(QR\) (from \(x = 0\) to \(x = 4\)) has a length of \(4\) units. For parallelogram \(Q'R'S'T'\), if we consider \(Q'R'\) (from \(x = 0\) to \(x = 2\)) has a length of \(2\) units.

Step2: Calculate the scale factor

The formula for the scale factor \(k=\frac{\text{length of image side}}{\text{length of pre - image side}}\). Using the side lengths from Step 1, \(k = \frac{2}{4}\)

Answer:

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