Coordinate geometry is an unusual way to do this but OK; it can be done.
Firstly, you need to choose your triangle.
I'd keep things simple by having the base going from (0,0) to (2,0).
That makes the midpoint of the base at (1,0)
The vertex will be at (2cos60, 2sin60) = (1,√ 3)
The median joins the midpoint of the base to the vertex so that is the line x=1, which is at right angles to the base.