Question

the triangle bcd is a dilation of the triangle bcd. 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 corresponding sides

Let's consider side $B'C'$ and side $BC$. The length of $B'C'$ can be found using the distance formula for two - points $(x_1,y_1)$ and $(x_2,y_2)$: $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $B'(- 2,2)$ and $C'(-4,2)$, $B'C'=\vert-2-(-4)\vert = 2$. For $B(8,-4)$ and $C(-8,-4)$, $BC=\vert8-(-8)\vert=16$.

Step2: Calculate scale factor

The scale factor $k$ of a dilation is given by the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. So $k=\frac{B'C'}{BC}=\frac{2}{16}=\frac{1}{8}$.

Answer:

$\frac{1}{8}$