Question

quadrilateral qrst is dilated and translated to form similar figure qrst. what is the scale factor for the dilation?

Explanation:

Step1: Find the length of a side in the original figure

For example, let's consider side \(QR\). Counting the units on the \(x -\)axis, \(QR = 6\) units (from \(x=- 1\) to \(x = 5\)).

Step2: Find the length of the corresponding side in the dilated figure

Consider side \(Q'R'\). Counting the units on the \(x -\)axis, \(Q'R'=2\) units (from \(x=-1\) to \(x = 1\)).

Step3: Calculate the scale factor

The formula for the scale factor \(k\) of a dilation is \(k=\frac{\text{length of side in dilated figure}}{\text{length of side in original figure}}\). So \(k = \frac{Q'R'}{QR}=\frac{2}{6}=\frac{1}{3}\)

Answer:

\(\frac{1}{3}\)