Question

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

Explanation:

Step1: Count side - lengths on grid

Count the number of grid units for each side. Let's assume each grid unit is 1. For side $EF$, if we count the grid units between $E$ and $F$, say $EF = 6$. And $E'F'=3$. So $\frac{E'F'}{EF}=\frac{3}{6}=\frac{1}{2}$.

Step2: Count $FG$ and $F'G'$

Count the grid - units for $FG$ and $F'G'$. Suppose $FG = 4$ and $F'G' = 2$. Then $\frac{F'G'}{FG}=\frac{2}{4}=\frac{1}{2}$.

Step3: Count $GH$ and $G'H'$

Count the grid - units for $GH$ and $G'H'$. Assume $GH = 2$ and $G'H' = 1$. Then $\frac{G'H'}{GH}=\frac{1}{2}$.

Answer:

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