Question

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

Explanation:

Step1: Determine the length of a side of the original figure

Let's consider the length of side \(QR\). If we assume the distance between two consecutive grid points is \(1\) unit. The length of \(QR\) (original figure) is \(4\) units.

Step2: Determine the length of the corresponding side of the dilated figure

The length of the corresponding side \(Q'R'\) (dilated figure) is \(2\) units.

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in dilated figure}}{\text{length of side in original figure}}\). So, \(k = \frac{2}{4}=\frac{1}{2}\)

Answer:

$\frac{1}{2}$