if cricle X is constructed so that it has a circumference of 120 centimeters, and is dilated to create circle X' with a circumference of 90 centimeters, then what is the scale factor? enter any non-whole number as a fraction

Answer 1

To find the scale factor between the two circles, we can use the ratio of their circumferences.

Given:

• Circumference of circle \( X \) = 120 centimeters
• Circumference of circle \( X' \) = 90 centimeters

The scale factor \( k \) can be calculated using the formula:

\[ k = \frac{\text{Circumference of } X'}{\text{Circumference of } X} \]

Substituting the values:

\[ k = \frac{90}{120} \]

Now, we can simplify the fraction:

\[ k = \frac{90 \div 30}{120 \div 30} = \frac{3}{4} \]

So, the scale factor is \( \frac{3}{4} \).