Question

the parallelogram bcde is a dilation of the parallelogram bcde. 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 side lengths

For example, consider the horizontal - side lengths of the two parallelograms. The length of side $BC$ in parallelogram $BCDE$: The $x$ - coordinates of $B(-4,4)$ and $C(4,4)$, so $BC=\vert4 - (-4)\vert=8$. The length of side $B'C'$ in parallelogram $B'C'D'E'$: The $x$ - coordinates of $B'(-1,2)$ and $C'(1,2)$, so $B'C'=\vert1-(-1)\vert = 2$.

Step2: Calculate the scale factor

The scale factor $k$ of a dilation is given by the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. So $k=\frac{B'C'}{BC}$. Substituting the values we found: $k=\frac{2}{8}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$