Question

1. two circles have radii ( r_1 = 7 ) and ( r_2 = 21 ). what is the scale factor (( k )) for the dilation?

a. 3
b. 2
c. 4.25
d. 2.5

Explanation:

Step1: Recall Scale Factor Formula

The scale factor \( k \) for dilation between two similar figures (like circles) is the ratio of the corresponding lengths (radii here). So \( k=\frac{r_2}{r_1} \) or \( k = \frac{r_1}{r_2} \), depending on direction. But since dilation from \( r_1 = 7 \) to \( r_2 = 21 \), we use \( k=\frac{r_2}{r_1} \).

Step2: Calculate Scale Factor

Substitute \( r_1 = 7 \) and \( r_2 = 21 \) into the formula: \( k=\frac{21}{7}=3 \).

Answer:

a. 3