Question

the triangle lmn is a dilation of the triangle lmn. what is the scale factor of the dilation?

Explanation:

Step1: Select a corresponding side

Let's consider side $LN$ and $L'N'$. The coordinates of $L(-10,0)$, $N(-10,10)$, $L'(-2,0)$ and $N'(-2,2)$.

Step2: Calculate the lengths of the sides

The length of $LN$ is $|10 - 0|=10$ (using the distance formula for points with the same $x -$coordinate, $d = |y_2 - y_1|$). The length of $L'N'$ is $|2 - 0| = 2$.

Step3: Find the scale factor

The scale factor $k$ of a dilation is given by the ratio of the length of the corresponding side of the image to the length of the corresponding side of the pre - image. So $k=\frac{L'N'}{LN}=\frac{2}{10}=\frac{1}{5}$.

Answer:

$\frac{1}{5}$