To determine the scale factor between the circles drawn by Horatio and Kelli, we start by looking at their radii.
Horatio's circle has a radius of [tex]\(6 \text{ xm}\)[/tex].
Kelli's circle has a radius of [tex]\(18 \text{ ym}\)[/tex].
The scale factor is the ratio of the radius of Horatio's circle to the radius of Kelli's circle. To find this, we divide Horatio's radius by Kelli's radius.
[tex]\[
\text{Scale factor} = \frac{\text{Horatio's radius}}{\text{Kelli's radius}} = \frac{6 \text{ xm}}{18 \text{ ym}}
\][/tex]
Simplifying this fraction:
[tex]\[
\frac{6}{18} = \frac{1}{3}
\][/tex]
Thus, the scale factor between Horatio's circle and Kelli's circle is:
[tex]\[
\frac{1}{3}
\][/tex]
This matches one of the provided choices. Therefore, the answer is:
[tex]\(\frac{1}{3}\)[/tex].
