This should be quite simple, though I'm having a hard time visualizing the solution. I'll have to just work it through.
We need m[xz] = DeltaX / DeltaZ = (x1 - x2) / (z1 - z2) and m[yz] = DeltaY / DeltaZ = (y1 - y2) / (z1 - z2). Now we solve for z = 0 ... but exactly how is that done?
Beginning at some point on the line, the line travels a certain distance in the direction of the x axis for every unit of distance it travels in the direction of the z axis, and that distance is m[xz]. If xa is the original point, xb is the point arrived at after traveling b units along the z axis. The solution is with in reach. za is some value, and zb is 0, and the distance traveled is either b or -b, but which one?
If we select, as Pa, P1, and as Pb: (xb, yb, 0), then m[xz] = (x1 - xb) / (z1 - 0). This answers our original question without requiring an answer to the question of the last paragraph. The latter remains unanswered in my mind, but I can see it is implicitly answered by the above equation, which can now be solved for xb.
So we now have two points on the x - y axial plane, Pb1 and Pb2 (base - points). As a reminder, we are attempting to locate the intersections of a line and a plane using formulae for the two geometries, and here we are attempting to derive a formula for the plane. The two base - points describe a line on the x - y plane, and that line is the basis for writing an equation for a plane which intersects the x - y plane to form that line.
