Question

the parallelogram efgh is a dilation of the parallelogram efgh. 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: Select a side to compare

Let's consider side EF and E'F'.

Step2: Find the length of EF

The endpoints of EF are E(-2, 2) and F(2, 2). Using the distance formula for horizontal line (since y - coordinates are the same), the length of EF is $|2 - (-2)|=4$.

Step3: Find the length of E'F'

The endpoints of E'F' are E'(-6, 5) and F'(8, 5). Using the distance formula for horizontal line (since y - coordinates are the same), the length of E'F' is $|8 - (-6)| = 14$.

Step4: Calculate the scale factor

The scale factor $k$ of a dilation is given by the ratio of the length of the dilated side to the length of the original side. So $k=\frac{\text{length of E'F'}}{\text{length of EF}}=\frac{14}{4}=\frac{7}{2}$.

Answer:

$\frac{7}{2}$