Finding a point on triangle.

Question

I have a non-right triangle with known x,y coordinates. Lets say A,B,C is the points of triangle. I want to find a new point D which is perpendicular line from point B and lies on the line AC. Any simpled questions for D(x,y)?

Answer 1

First, given coordinates of $A$ and $C$, you can have the formula of the line $AC$.

Secondly, we know that line $BD$ and $AC$ are perpendicular, so we can get the slope of $BD$ (the product of slopes of perpendicular lines in $\mathbb R^2$ is $-1$). With coordinates of $B$, we can then get the formula of $BD$. And $D$ is just the point of intersection of $AC$ and $BD$.