Concerning pointless: The angle of Y/X is the Tangent
(Tan) of the line. If you remember your trig, as you approach the vertical and X gets smaller, the result of
Y/X becomes very large. When X becomes zero, the result
use to be defined as infinite, but now I understand it is
just considered undefined. That means you have to have a
separate check to make sure that X is not zero, and have a
different expression if it is. That, plus the fact that
Y/X involves division, a much slower process than using
multiplication, means two strikes against this approach. But many people use it, simply because it is sort of self-evident if you are familiar with any graphing at all. You might recall that parallel lines have the same slope, and if they have the same C value, as in Y=mX+C, then they lie along the same line. But again, you have a situation where the length of the line is assumed to be infinite, and yet the point will not be on the line if it lies beyond the lines given end points. The distance approach resolves all those issues pretty well.
(Tan) of the line. If you remember your trig, as you approach the vertical and X gets smaller, the result of
Y/X becomes very large. When X becomes zero, the result
use to be defined as infinite, but now I understand it is
just considered undefined. That means you have to have a
separate check to make sure that X is not zero, and have a
different expression if it is. That, plus the fact that
Y/X involves division, a much slower process than using
multiplication, means two strikes against this approach. But many people use it, simply because it is sort of self-evident if you are familiar with any graphing at all. You might recall that parallel lines have the same slope, and if they have the same C value, as in Y=mX+C, then they lie along the same line. But again, you have a situation where the length of the line is assumed to be infinite, and yet the point will not be on the line if it lies beyond the lines given end points. The distance approach resolves all those issues pretty well.