Question

circle m dilated by a scale factor of 3 gives circle n. if the circumference of circle n is 6 cm, what is the circumference of circle m? a. 2 cm b. 18 cm c. 3 cm d. 54 cm

Explanation:

Step1: Recall dilation - circumference relationship

When a figure is dilated by a scale factor $k$, the ratio of the new - figure's circumference to the original - figure's circumference is equal to the scale factor. Let the circumference of circle $M$ be $C_M$ and the circumference of circle $N$ be $C_N$. The scale factor $k = 3$. We know that $\frac{C_N}{C_M}=k$.

Step2: Rearrange the formula to solve for $C_M$

We can rewrite the formula $\frac{C_N}{C_M}=k$ as $C_M=\frac{C_N}{k}$. Given that $C_N = 6$ cm and $k = 3$.
Substitute the values into the formula: $C_M=\frac{6}{3}$.

Answer:

$2$ cm