Question

If you use a scale factor of 1/5
to create a circle with radius 18 cm, what is the radius of the original circle you dilated?
Responses

180 cm
180 cm - no response given
90 cm
90 cm - not selected, this is the correct answer
9 m
9 m - no response given
3.6 cm

Answer 1

To find the radius of the original circle before dilation, you can use the formula for dilation, which states:

\[
\text{New radius} = \text{Original radius} \times \text{Scale factor}
\]

In this case, you have the new radius as 18 cm and the scale factor as \( \frac{1}{5} \). You can rearrange the formula to find the original radius:

\[
\text{Original radius} = \frac{\text{New radius}}{\text{Scale factor}}
\]

Substituting in the known values:

\[
\text{Original radius} = \frac{18 \text{ cm}}{1/5} = 18 \text{ cm} \times 5 = 90 \text{ cm}
\]

Therefore, the radius of the original circle you dilated is **90 cm**.