Question

the rectangle qrst is a dilation of the rectangle qrst. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Find length of QR

The length of $QR$ is the vertical distance from $Q(9,2)$ to $R(9,-10)$.
$QR = |2 - (-10)| = 12$

Step2: Find length of Q'R'

The length of $Q'R'$ is the vertical distance from $Q'(5,1)$ to $R'(5,-5)$.
$Q'R' = |1 - (-5)| = 6$

Step3: Calculate scale factor

Scale factor is $\frac{\text{Image length}}{\text{Pre-image length}}$.
$\text{Scale factor} = \frac{Q'R'}{QR} = \frac{6}{12} = \frac{1}{2}$

Answer:

$\frac{1}{2}$