Question

two figures are shown in the coordinate plane. determine whether one figure is a dilation of the other.
\\(\frac{ef}{ef}=\frac{4}{7}\\) \\(\frac{fg}{fg}=\frac{1}{4}\\)
\\(\frac{gh}{gh}=\frac{2}{2}\\) \\(\frac{hi}{hi}=\frac{2}{4}\\)

1. are the figures dilations of each other?

complete the statement.

1. the fractions? equivalent,

so the figures are dilations of each other.
are not

Explanation:

Step1: Recall dilation property

In a dilation, the ratios of corresponding - side lengths are equal.

Step2: Compare given ratios

We have $\frac{E'F'}{EF}=\frac{4}{7}$, $\frac{F'G'}{FG}=\frac{1}{4}$, $\frac{G'H'}{GH}=\frac{2}{2} = 1$, $\frac{H'I'}{HI}=\frac{2}{4}=\frac{1}{2}$. Since $\frac{4}{7}
eq\frac{1}{4}
eq1
eq\frac{1}{2}$, the ratios of the corresponding - side lengths are not equal.

Answer:

The fractions are not equivalent, so the figures are not dilations of each other.