Question

the trapezoid cdef is a dilation of the trapezoid cdef. 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: Identify corresponding side lengths

First, find the length of a side of the original trapezoid and its dilated counterpart. For example, side $CF$: $C$ is at $(-10,0)$, $F$ is at $(-10,10)$, so length $CF = 10 - 0 = 10$. Side $C'F'$: $C'$ is at $(-2,0)$, $F'$ is at $(-2,2)$, so length $C'F' = 2 - 0 = 2$.

Step2: Calculate scale factor

Scale factor is the ratio of the dilated side length to the original side length.
$\text{Scale factor} = \frac{\text{Length of dilated side}}{\text{Length of original side}} = \frac{C'F'}{CF} = \frac{2}{10} = \frac{1}{5}$

Answer:

$\frac{1}{5}$