In this question you will derive a general formula for the distance of a point from a line. Let $P$ be the point $(p,q)$ and $L$ the line $y = m x + b$.

The slope of $L$ is .

The slope of a line perpendicular to $L$ is .

The line through $P$ perpendicular to $L$ can be written as $y = s x + c$
where $s$ is:
and $c$ is: .
That line intersects $L$ in the point $Q = (u,v)$,

where $u$ is:
and $v$ is: .

The distance of $P$ and $Q$ is .

(Note, all answers must be in terms of $m$, $b$, $p$ and $q$.)
Hint: If you are bewildered by all the symbols ask yourself what they mean in the special cases of the preceding home work, and compare your calculations for this problem with the numerical calculations you did earlier.