Question

two figures are shown in the coordinate plane. determine whether

$\frac{ab}{ab}=\frac{1}{2}$ $\frac{bc}{bc}=\frac{1}{2}$

$\frac{cd}{cd}=\frac{1}{2}$ $\frac{de}{de}=\frac{1}{2}$

1. are the figures dilations of each other?

complete the statement.

1. the fractions? equivalent,

so the figures? dilations of
each other.

Explanation:

Step1: Check fraction equality

We are given $\frac{A'B'}{AB}=\frac{1}{2}$, $\frac{B'C'}{BC}=\frac{1}{2}$, $\frac{C'D'}{CD}=\frac{1}{2}$, $\frac{D'E'}{DE}=\frac{1}{2}$. All the given fractions are equal.

Step2: Recall dilation property

For two figures to be dilations of each other, the ratios of corresponding side - lengths must be equal. Since the ratios of all corresponding side - lengths are $\frac{1}{2}$, the figures are dilations of each other.

Answer:

The fractions are equivalent, so the figures are dilations of each other.