Here's the question I am trying to solve-
The [points] $A$, $B$, $C$ have respective co-ordinates $(3, 4)$, $(-4, 3)$ and $(8, -6)$. Find the area of $\Delta ABC$ and the length of the perpendicular from $A$ on $BC$.
Now, calculating the area is the easy part. I can do that. But how do I get the length of the perpendicular drawn from A on BC?
Now, if it were a median, I could have found out the co-ordinates of the point where the line touches the side. But this is not a median, rather a perpendicular. How can I know where it touches the side?
Is there some special property that can help me solve this problem? What am I missing?
It's also obvious that the perpendicular creates two Right triangles. That somehow helpful?