Question

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

Explanation:

Step1: Count side - lengths on grid

Count the number of grid - units for each side of the two figures. For example, if $EF$ is 4 grid - units long and $E'F'$ is 2 grid - units long.

Step2: Calculate the fractions

For $\frac{E'F'}{EF}$, if $E'F' = 2$ and $EF=4$, then $\frac{E'F'}{EF}=\frac{2}{4}=\frac{1}{2}$. Do the same for other pairs. Assume we find the lengths of other corresponding sides in the same way. If $F'G' = 1$ and $FG = 2$, then $\frac{F'G'}{FG}=\frac{1}{2}$. If $G'H'=1$ and $GH = 2$, then $\frac{G'H'}{GH}=\frac{1}{2}$. If $H'I'=1$ and $HI = 2$, then $\frac{H'I'}{HI}=\frac{1}{2}$.

Answer:

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