Question

the parallelogram uvwx is a dilation of the parallelogram uvwx. 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 corresponding sides

Let's consider the horizontal sides of the parallelograms. Side $VW$ in parallelogram $UVWX$ has endpoints $V(2,5)$ and $W(4,5)$, so its length is $4 - 2=2$. Side $V'W'$ in parallelogram $U'V'W'X'$ has endpoints $V'(4,10)$ and $W'(8,10)$, so its length is $8 - 4 = 4$.

Step2: Calculate scale - factor

The scale factor $k$ of a dilation is given by the ratio of the length of a side in the dilated figure to the length of the corresponding side in the original figure. So $k=\frac{\text{length of side in }U'V'W'X'}{\text{length of corresponding side in }UVWX}=\frac{4}{2}=2$.

Answer:

$2$