Question

circle l is dilated to create circle m, as shown. what is the scale factor of the dilation?

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ of a dilation is given by the ratio of the corresponding lengths of the dilated figure to the original figure. For circles, we can use the ratio of their diameters.
Let $d_1$ be the diameter of circle $L$ and $d_2$ be the diameter of circle $M$. Here, $d_1 = 5$ and $d_2=12$.
The formula for the scale factor $k=\frac{d_2}{d_1}$.

Step2: Calculate the scale factor

Substitute $d_1 = 5$ and $d_2 = 12$ into the formula: $k=\frac{12}{5}=2.4$

Answer:

$2.4$