Question

If the circumference of circle X is 12π and the circumference of circle Z is 6π , then what is the scale factor from X to Z ?(1 point)
Responses

2:1
ratio of 2 to 1

1:3
ratio of 1 to 3

1:2
ratio of 1 to 2

3:1
ratio of 3 to 1

Answer 1

To determine the scale factor from circle X to circle Z based on their circumferences, you can use the following relationship:

1. **Circumference of Circle X:** \( C_X = 12\pi \)
2. **Circumference of Circle Z:** \( C_Z = 6\pi \)

The scale factor (SF) between the two circles can be calculated by dividing the circumference of circle X by the circumference of circle Z:

\[
\text{Scale Factor} = \frac{C_X}{C_Z} = \frac{12\pi}{6\pi} = \frac{12}{6} = 2
\]

This means that for every unit of measurement in circle Z, circle X is 2 units.

Therefore, the scale factor from circle X to circle Z is **2:1**.

The correct response is:
*2:1
*ratio of 2 to 1*