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 1:2 ratio of 1 to 2 2:1 ratio of 2 to 1 1:3 ratio of 1 to 3 3:1

Answer 1

To find the scale factor from circle X to circle Z based on their circumferences, we can use the following steps:

1. The circumference of circle X is 12π.
2. The circumference of circle Z is 6π.

The scale factor can be calculated by taking the ratio of the circumferences:

\[ \text{Scale Factor} = \frac{\text{Circumference of Circle X}}{\text{Circumference of Circle Z}} = \frac{12\pi}{6\pi} = \frac{12}{6} = 2 \]

This means that circle X is 2 times larger than circle Z, or conversely, the scale factor from circle X to circle Z is:

\[ \text{Scale Factor} = \frac{1}{2} \]

In terms of ratios, this can be expressed as a ratio of 2:1, indicating that for every 2 units in circle X, there is 1 unit in circle Z.

Therefore, the correct answer is:

2:1 ratio of 2 to 1.