If circle X

Question

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

Answer 1

The scale factor for dilations can be found by comparing the circumferences of the two circles.

The circumference of circle \( X \) is given as 120 centimeters, and the circumference of circle \( X' \) after dilation is given as 90 centimeters.

To find the scale factor \( k \), you can use the formula:

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

Substituting the given values:

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

Now simplify the fraction:

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

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