Question

You use scale factor of 3/4 to create a dilated circle with a radius of 9 inches. What is the radius of the original circle?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the radius of the original circle, we can use the formula for dilation:

\[ \text{dilated radius} = \text{scale factor} \times \text{original radius} \]

Let's plug in the given values:

\[ 9 \text{ inches} = \frac{3}{4} \times \text{original radius} \]

To solve for the original radius, we can rearrange the equation:

\[ \text{original radius} = \frac{9 \text{ inches}}{\frac{3}{4}} = \frac{9 \text{ inches} \times 4}{3} = \frac{36}{3} \text{ inches} = \boxed{12 \text{ inches}} \]

Therefore, the radius of the original circle is 12 inches.