Finding coordinates of Koch curve

Sorry for my language since english is my second language. I am trying to convert a straight line into a fractal which is Koch curve. the 2 points of the straight line are given and then need to create the koch curve where I divide the line to 3 segments and then make the second segment a equilateral triangle.
so far we convert the straight lne to 4 equally segments and I need to figure out all the coordinates of koch curve.
I have thought of a straight line when the y coordinates of the 2 point are the same which give me horizontal line. if so, I can figure out the 3 points of equilateral triangle by dividing the second segment half and taking the cos(60) of the right triangle.
My problem is how to find all coordinates when the stright line is diagonal, for example a(200,100), b(400,600) or a(400,500), b(100,500).
Hope someone can help me in this.