Question

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use the keypad to enter your answers in the boxes. express your answer in the simplest fraction form.
the scale factor from circle m to circle n is
the scale factor from circle n to circle m is

Explanation:

Step1: Recall scale - factor formula

The scale factor from one figure to another is the ratio of the corresponding lengths. For circles, we can use the ratio of the radii. Let the radius of circle $M$ be $r_M = 12$ units and the radius of circle $N$ be $r_N=\frac{3}{2}$ units.

Step2: Calculate scale - factor from $M$ to $N$

The scale factor from circle $M$ to circle $N$, denoted as $k_{M
ightarrow N}$, is given by the ratio $\frac{r_N}{r_M}$. So, $k_{M
ightarrow N}=\frac{\frac{3}{2}}{12}=\frac{3}{2}\times\frac{1}{12}=\frac{3}{24}=\frac{1}{8}$.

Step3: Calculate scale - factor from $N$ to $M$

The scale factor from circle $N$ to circle $M$, denoted as $k_{N
ightarrow M}$, is the reciprocal of the scale factor from $M$ to $N$. So, $k_{N
ightarrow M}=\frac{r_M}{r_N}=\frac{12}{\frac{3}{2}} = 12\times\frac{2}{3}=8$.

Answer:

The scale factor from circle $M$ to circle $N$ is $\frac{1}{8}$.
The scale factor from circle $N$ to circle $M$ is $8$.