Question

quadrilaterals m and n are similar.
a. what is the scale factor of the dilation that takes m to n?
type your answer in the box.
b. what is the scale factor of the dilation that takes n to m?
type your answer in the box.

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ of a dilation from figure $A$ to figure $B$ is given by $k=\frac{\text{corresponding side length in }B}{\text{corresponding side length in }A}$.

Step2: Find scale factor from $M$ to $N$

Let's take the side of length $5$ in $N$ and the corresponding side of length $12.5$ in $M$. Then $k_{M - N}=\frac{5}{12.5}=\frac{5\times2}{12.5\times2}=\frac{10}{25}=\frac{2}{5} = 0.4$.

Step3: Find scale factor from $N$ to $M$

The scale factor from $N$ to $M$ is the reciprocal of the scale factor from $M$ to $N$. So $k_{N - M}=\frac{12.5}{5}=2.5$.

Answer:

a. $0.4$
b. $2.5$