If the circle is dilated by a factor 4 then the radius becomes [tex]4\sqrt{2}[/tex] units.
What is area?
Area is the quantity that shows the extent of surface covered. Area of circle is π[tex]r^{2}[/tex]. where r is radius.
How to find the radius of circle?
Before dilation the radius will be [tex]\sqrt{(0-0)^{2} +(4-0)^{2} }[/tex]
=[tex]\sqrt{16}[/tex]
=4 units.
If the circle is dilated by factor of 4 then the area will increase byπ [tex](4)^{2}[/tex]=16π
Area before dilation =16π .
Area after dilation=16π+16π=32π.
π[tex]r^{2}[/tex]=32π
[tex]r^{2}[/tex]=32
r=[tex]4\sqrt{2}[/tex]units.
Hence the distance equal to radius is 4[tex]\sqrt{2}[/tex] units.
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