Question

the square qrst is a dilation of the square 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

Explanation:

Step1: Identify side length of QRST

First, find the length of one side of the original square QRST. For example, the horizontal distance from Q(-2,1) to R(0,1) is $|0 - (-2)| = 2$.

Step2: Identify side length of Q'R'S'T'

Next, find the length of the corresponding side of the dilated square Q'R'S'T'. The horizontal distance from Q'(-8,4) to R'(0,4) is $|0 - (-8)| = 8$.

Step3: Calculate scale factor

The scale factor is the ratio of the dilated side length to the original side length.
$\text{Scale Factor} = \frac{\text{Length of } Q'R'}{\text{Length of } QR} = \frac{8}{2} = 4$

Answer:

$4$