Finding a point on the line perpendicular to a line from another point I'm sorry if this is kind of basic, it's been a while since I took geometry. I did find this answer, but it requires 4 points and I only have 3.
I have three points $A$, $B$ and $C$ that form a non-right triangle. I know the Cartesian coordinates of these three points. Suppose I draw a perpendicular from $B$ through $AC$ where $D$ is the point where the perpendicular intersects $AC$. How can I find the Cartesian coordinates of a point $T$ along $\overrightarrow {BD}$ that is $n$ beyond $D$?
I drew a diagram to demonstrate what I'm trying to find.
Diagram

Any help would be appreciated, thanks!

To find $DA$ it is enough to calculate the dot product of $BA$ and $CA$.
$$D-A = \frac{(C-A)}{|C-A|}\cdot\frac{\langle B-A,C-A\rangle}{|C-A|} = (C-A)\cdot\frac{\langle B-A,C-A\rangle}{\langle C-A, C-A\rangle}.$$
If you want a better intuition why this works, check out the Gram-Schmidt orthogonalization.
When you have $D = A + (D-A)$, you can find $T$ by extending $BD$ from $D$ for a desired length
$$T = D+n\cdot\frac{(D-B)}{|D-B|}.$$
I hope this helps $\ddot\smile$
