triangle jkl was dilated using the rule $d_{m,\frac{1}{3}}$. the image, triangle jkl, is the result of the…

Explanation:

Step1: Recall dilation property

The scale - factor of dilation is $k = \frac{1}{3}$. Let $ML=x$ and $ML' = y$. We know that $y=\frac{1}{3}x$. Also, $ML - ML'=L'L$. Given $ML' = 2.5$ units.

Step2: Find the length of $ML$

Since $ML'=\frac{1}{3}ML$, then $ML = 3\times ML'$. Substituting $ML' = 2.5$ units, we get $ML=3\times2.5 = 7.5$ units.

Step3: Calculate $L'L$

$L'L=ML - ML'$. Substituting $ML = 7.5$ units and $ML' = 2.5$ units, we have $L'L=7.5 - 2.5=5$ units.

Answer:

5 units