Answer
$(b, \frac{ab-b^2}{c})$
Work Step by Step
We first describe the slope. Using the knowledge of the point we are looking for, we see that the equation of the line is:
$ y=\frac{a-b}{c}x$
We find the slope of one of the lines is:
c/b
Since this is perpendicular to the other line being considered, we find that the slope of that line is:
-b/c
(a,0) is on this line, which means the equation of the line can be described as:
$y=-b/c(x-a)$
We equate these two equations to have:
$\frac{a-b}{c}x=-b/c(x-a)$
Upon solving, we find:
x =b
We substitute back into the equation to find y:
$ y = \frac{ab-b^2}{c}$
This gives the point:
$(b, \frac{ab-b^2}{c})$
