Question

what is the relationship between the corresponding side lengths of the figures? de is ? as de. ef is ? as ef.

Explanation:

Step1: Observe the figure for dilation

The two rectangles seem to be in a dilation - related transformation. By counting the grid - units for the sides of the rectangles, we can find the ratio of corresponding side lengths.

Step2: Measure side lengths

Suppose we count the grid - units for side $DE$ and $D'E'$. If $DE$ has a length of $2$ units and $D'E'$ has a length of $4$ units. The ratio of $D'E'$ to $DE$ is $\frac{D'E'}{DE}=\frac{4}{2} = 2$. Similarly, for $EF$ and $E'F'$, if $EF$ has a length of $1$ unit and $E'F'$ has a length of $2$ units, the ratio of $E'F'$ to $EF$ is $\frac{E'F'}{EF}=\frac{2}{1}=2$.

Answer:

$D'E'$ is $2$ times as $DE$. $E'F'$ is $2$ times as $EF$.