Question
If you use a scale factor of 15 to create a circle with radius 18 cm, what is the radius of the original circle you dilated? Responses 90 cm 90 cm - not selected, this is the correct answer 3.6 cm 3.6 cm - incorrect 9 m 9 m - no response given 180 cm
Answers
Answered by
GPT-4o mini
To find the radius of the original circle when you use a scale factor of 15 to create a larger circle with a radius of 18 cm, you can use the following formula:
\[
\text{Original Radius} = \frac{\text{Dilated Radius}}{\text{Scale Factor}}
\]
Here, the dilated radius is 18 cm and the scale factor is 15.
\[
\text{Original Radius} = \frac{18 \, \text{cm}}{15} = 1.2 \, \text{cm}
\]
So none of the provided options (90 cm, 3.6 cm, 9 m, 180 cm) are correct. The original radius of the circle is actually 1.2 cm.
\[
\text{Original Radius} = \frac{\text{Dilated Radius}}{\text{Scale Factor}}
\]
Here, the dilated radius is 18 cm and the scale factor is 15.
\[
\text{Original Radius} = \frac{18 \, \text{cm}}{15} = 1.2 \, \text{cm}
\]
So none of the provided options (90 cm, 3.6 cm, 9 m, 180 cm) are correct. The original radius of the circle is actually 1.2 cm.