**Theorem
1.11**: The
perpendicular
distance from the
point

to the line

is

**Proof**: We need only use the
distance formula to
find the distance from
the point (*x*_{1},
*y*_{1}) to its foot
in the line *y* = *mx* + *b*, which, by Theorem
1.10, is

So the distance is

We will need to find common denominators.

or

We can factor an * m* out of all the terms on the top of the first
square.

Incredibly, the terms on the top of the second square are all negatives of the terms of the top of the first square, but that does not matter because they are being squared. So we can factor out the common square factors, and take their square roots outside the radical.

It will prove to be more useful to irrationalize the numerator.