Question

the triangle lmn is a dilation of the triangle lmn. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

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 $LN$ using the distance formula for two - points $(x_1,y_1)$ and $(x_2,y_2)$ which is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $L(-10,0)$ and $N(-10,10)$, $x_1=-10,y_1 = 0,x_2=-10,y_2 = 10$, so $LN=\sqrt{(-10+10)^2+(10 - 0)^2}=10$. For $L'(-2,0)$ and $N'(-2,2)$, $x_1=-2,y_1 = 0,x_2=-2,y_2 = 2$, so $L'N'=\sqrt{(-2 + 2)^2+(2-0)^2}=2$.

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:

$\frac{1}{5}$