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: Find the length of a corresponding side in the original and dilated trapezoid

In trapezoid \(CDEF\), let's consider the horizontal side \(CD\). The \(x\) - coordinate of \(C\) is \(2\) and the \(x\) - coordinate of \(D\) is \(- 2\). So the length of \(CD\) is \(|2-(-2)|=4\).
In trapezoid \(C'D'E'F'\), the \(x\) - coordinate of \(C'\) is \(4\) and the \(x\) - coordinate of \(D'\) is \(-4\). So the length of \(C'D'\) is \(|4 - (-4)|=8\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of corresponding side in pre - image}}\).
Substituting the values, we get \(k = \frac{8}{4}=2\).

Answer:

$2$