Question

the parallelogram lmno is a dilation of the parallelogram lmno. what is the scale factor of the dilation?

Explanation:

Step1: Select corresponding sides

Choose side $LM$ and $L'M'$. Co - ordinates of $L(- 5,0)$ and $M(-2,4)$, $L'(-10,0)$ and $M'(-4,8)$.

Step2: Calculate length of side $LM$

Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $L(-5,0)$ and $M(-2,4)$, $d_{LM}=\sqrt{(-2+5)^2+(4 - 0)^2}=\sqrt{3^2+4^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Step3: Calculate length of side $L'M'$

For $L'(-10,0)$ and $M'(-4,8)$, $d_{L'M'}=\sqrt{(-4 + 10)^2+(8 - 0)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10$.

Step4: Find the scale factor

The scale factor $k=\frac{d_{L'M'}}{d_{LM}}$. Substituting the values, $k=\frac{10}{5}=2$.

Answer:

$2$