Fınding the position of a point on the line

[Arman777]

Let us suppose we have a line $l_1 = ax + by + c = 0$ and we have a point P, $P(x_p, y_p)$ that is outside of this line. If we draw a perpendicular line from point $P$ to a point on the $l_1$. What would be the coordinates of this point ? I know there are many ways to do it. But I am looking for a single equation that can describe this point ($Q$) ?

 

[pasmith]

Have you considered using one of those methods to solve the problem, which should give you an expression for $Q$ in terms of $P$ and $l_1$?