If circle 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 determine the scale factor between circle X and circle X′ based on their circumferences, we can use the formula for scale factor, which is the ratio of the new circumference to the original circumference.

Given:

• Circumference of circle X = 120 cm
• Circumference of circle X′ = 90 cm

The scale factor \( k \) can be calculated as follows:

\[ k = \frac{\text{Circumference of } X'}{\text{Circumference of } X} = \frac{90}{120} \]

Now, simplify \( \frac{90}{120} \):

\[ k = \frac{3}{4} \]

Thus, the scale factor is:

\[ \boxed{\frac{3}{4}} \]