Question

two figures are shown in the coordinate plane. determine whether one figure is a dilation. write a fraction for each pair of corresponding side lengths.
$\frac{ef}{ef}=\frac{4}{7}$
$\frac{fg}{fg}=\frac{1}{2}$
$\frac{gh}{gh}=\frac{1}{2}$
$\frac{hi}{hi}=\frac{1}{2}$
$\frac{ef}{ef}=\frac{4}{7}$

Explanation:

Step1: Count grid - squares for side lengths

Count the number of grid - squares for each corresponding side in the two figures. For example, if $EF$ spans 7 grid - squares and $E'F'$ spans 4 grid - squares, then $\frac{E'F'}{EF}=\frac{4}{7}$.

Step2: Do the same for other sides

For side $FG$, if $FG$ spans 2 grid - squares and $F'G'$ spans 1 grid - square, then $\frac{F'G'}{FG}=\frac{1}{2}$. Similarly, for $GH$ and $G'H'$, and $HI$ and $H'I'$, we find $\frac{G'H'}{GH}=\frac{1}{2}$ and $\frac{H'I'}{HI}=\frac{1}{2}$ by counting the grid - squares.

Answer:

$\frac{E'F'}{EF}=\frac{4}{7}$, $\frac{F'G'}{FG}=\frac{1}{2}$, $\frac{G'H'}{GH}=\frac{1}{2}$, $\frac{H'I'}{HI}=\frac{1}{2}$