Question

triangle jkl was dilated using the rule $d_{m,\frac{1}{3}}$. the image, triangle jkl, is the result of the dilation. what is ll? 5 units 7.5 units 10 units 12.5 units 2.5

Explanation:

Step1: Recall dilation formula

The scale - factor of dilation is $k = \frac{1}{3}$. If a point $P$ is dilated from a center $M$ to get $P'$, then the distance between the center of dilation $M$ and the original point $P$ and the distance between the center of dilation $M$ and the dilated point $P'$ are related by $MP'=k\times MP$. Let $ML = x$ and $ML'=\frac{1}{3}x$. Also, we know that $ML - ML'=L'L$.

Step2: Assume $ML = x$

We know that $ML' = 2.5$ units and since $ML'=\frac{1}{3}ML$, then $ML=3\times ML'$. So $ML = 3\times2.5=7.5$ units.

Step3: Calculate $L'L$

$L'L=ML - ML'$. Substitute $ML = 7.5$ units and $ML' = 2.5$ units. Then $L'L=7.5 - 2.5 = 5$ units.

Answer:

5 units