He unit circle has a radius of 1 unit and is centered at the origin. it is dilated so that it passes through the point (4, 0). what is the scale factor of dilation?

We know that

if the dilated circle passes through the point (4, 0)
so
the new radius is the distance from the origin to point (4,0)
d=√[(4-0)²+0²]> d=√16> d=4 units

the new radius  is 4 units
original radius is 1 units

[new radius]=[scale]*[original radius]
scale=new radius/original radius> scale=4/1> 4

the answer is
the scale factor of dilation is 4