Question

1. the circle is dilated by a scale factor of 1.05. what is the radius of the new circle? was the dilation an enlargement or reduction?

Explanation:

Step1: Calculate the radius of the new circle

The formula for the radius of the new circle after dilation is \(r_{new}=r_{original}\times scale - factor\). Given \(r_{original} = 20m\) and scale - factor \(= 1.05\).

$$r_{new}=20\times1.05$$

$$r_{new}=21m$$

Step2: Determine if it is an enlargement or reduction

Since the scale factor \(1.05> 1\), when the scale factor of a dilation is greater than \(1\), the dilation is an enlargement.

Answer:

The radius of the new circle is \(21m\) and the dilation is an enlargement.