To find the scale factor of the circles given the ratio of their diameters, let's analyze the question step-by-step:
1. Understand the given ratio:
The problem states that the ratio of the diameters of two circles is [tex]\( y \)[/tex] to [tex]\( z \)[/tex], which can be written as:
[tex]\[
\frac{\text{Diameter of Circle 1}}{\text{Diameter of Circle 2}} = \frac{y}{z}
\][/tex]
2. Identify what the scale factor of the circles represents:
The scale factor essentially tells us how one dimension (diameter, in this case) of one circle compares to the same dimension of the other circle. In simpler terms, it is the factor by which one circle's diameter is scaled to obtain the other circle’s diameter.
3. Analyze the possible choices given:
- [tex]\(\frac{y}{2z}\)[/tex]
This implies that the first circle's diameter is half the ratio of the given diameters. This is not our given ratio.
- [tex]\(\frac{y}{z}\)[/tex]
This implies that the first circle's diameter is exactly the ratio of the given diameters. This matches with our understanding of the ratio.
- [tex]\(yz\)[/tex]
This would suggest that the scale factor is the product of the two diameters, which doesn’t reflect the concept of a ratio.
- [tex]\(2yz\)[/tex]
This would imply that the scale factor is twice the product of the two diameters, which again doesn’t logically represent the given ratio.
Given the correct ratio of the diameters [tex]\(\frac{y}{z}\)[/tex], the scale factor between the diameters of the two circles is directly:
[tex]\[
\frac{y}{z}
\][/tex]
Thus, the scale factor of the circles is:
[tex]\(\boxed{\frac{y}{z}}\)[/tex]
