Question

the rectangle htjk is a dilation of the rectangle hjk. 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 HK

The coordinates of $H$ are $(-8,0)$ and $K$ are $(4,0)$. Calculate the distance:
$HK = |4 - (-8)| = 12$

Step2: Find length of H'K'

The coordinates of $H'$ are $(-10,0)$ and $K'$ are $(5,0)$. Calculate the distance:
$H'K' = |5 - (-10)| = 15$

Step3: Calculate scale factor

Scale factor = $\frac{\text{Image length}}{\text{Pre-image length}}$
$\text{Scale factor} = \frac{15}{12} = \frac{3}{2}$

Answer:

$\frac{3}{2}$