Question

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

Explanation:

Step1: Choose a corresponding side

Let's consider the vertical side of the parallelograms. For example, the vertical distance from $T$ to $S$ and from $T'$ to $S'$. The $y -$ coordinate of $T$ is 6 and of $S$ is - 6, so the length of $TS=6 - (-6)=12$. The $y -$ coordinate of $T'$ is 8 and of $S'$ is - 8, so the length of $T'S'=8-(-8) = 16$.

Step2: Calculate the scale factor

The scale factor $k$ of a dilation is given by the ratio of the length of the corresponding side in the dilated figure to the length of the corresponding side in the original figure. So $k=\frac{T'S'}{TS}=\frac{16}{12}=\frac{4}{3}$.

Answer:

$\frac{4}{3}$