Question

the rectangle klmn is a dilation of the rectangle klmn. what is the scale factor of the dilation?

Explanation:

Step1: Identify side lengths

First, find the length of a side of rectangle $KLMN$ and its corresponding side in $K'L'M'N'$. For example, side $KL$: from $x=-8$ to $x=-4$, so length is $|-4 - (-8)| = 4$. Side $K'L'$: from $x=-4$ to $x=-2$, so length is $|-2 - (-4)| = 2$.

Step2: Calculate scale factor

The scale factor is the ratio of the image side length to the pre-image side length.
$\text{Scale factor} = \frac{\text{Length of } K'L'}{\text{Length of } KL} = \frac{2}{4} = \frac{1}{2}$

Answer:

$\frac{1}{2}$