Question

circle r has a radius of 5 units and undergoes a dilation to form circle s, whose radius is 15 units. which statement about the dilation from circle r to circle s is correct? the scale factor of the dilation from circle r to circle s is 1/3. circle s is three times the size of circle r. circle r was reduced to form circle s. the scale factor of the dilation from circle r to circle s is 3.

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ of a dilation is given by $k=\frac{\text{new length}}{\text{original length}}$. For circles, we can use the radii. Here, the original radius $r_R = 5$ and the new radius $r_S=15$.

Step2: Calculate the scale factor

$k=\frac{r_S}{r_R}=\frac{15}{5}=3$. This means circle $S$ is three times the size of circle $R$ as the scale - factor is 3.

Answer:

B. Circle $S$ is three times the size of circle $R$.
D. The scale factor of the dilation from circle $R$ to circle $S$ is 3.