Question

the triangle efg is a dilation of the triangle efg. 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 $FG$ and $F'G'$. The length of $FG$ can be found using the distance formula between $F(0,1)$ and $G(1,0)$. The length of $F'G'$ can be found between $F'(- 4,0)$ and $G'(4,0)$.

Step2: Calculate lengths

The length of $FG=\sqrt{(1 - 0)^2+(0 - 1)^2}=\sqrt{1 + 1}=\sqrt{2}$. The length of $F'G'=\vert4-(-4)\vert = 8$.

Step3: Find 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 $k=\frac{F'G'}{FG}=\frac{8}{\sqrt{2}}=\frac{8\sqrt{2}}{2} = 4\sqrt{2}$. But if we consider horizontal or vertical displacements for simplicity. Let's consider the $x$ - coordinates of $G$ and $G'$. The $x$ - coordinate of $G$ is $1$ and of $G'$ is $4$. The scale factor $k = 4$.

Answer:

$4$