calculating a scale factor\nquadrilateral qrst is dilated and translated to form similar figure qrst. what…

Explanation:

Step1: Identify corresponding side lengths

Let's consider the horizontal side lengths. For example, the length of side $QR$ in the original quadrilateral $QRST$: If we assume $Q=(0,0)$ and $R=(4,0)$, the length of $QR = 4$. In the dilated - translated figure $Q'R'S'T'$, if $Q'=(0,2)$ and $R'=(2,2)$, the length of $Q'R' = 2$.

Step2: Calculate the scale factor

The scale factor $k$ of a dilation is given by the ratio of the length of a side in the image to the length of the corresponding side in the pre - image. So, $k=\frac{\text{length of side in image}}{\text{length of corresponding side in pre - image}}=\frac{Q'R'}{QR}=\frac{2}{4}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$