Too Long; Didn't Read
Why would you care about some homogeneous coordinates, whatever they are? Well, if you work with geometry: 3D-graphics, image processing, physical simulation, the answer is obvious. Knowing the mathematics behind your framework of choice lets you write more efficient code. I once had to speed up one .NET application that bends pictures and simply re-implementing some primitive operations the right way <a href="https://leanpub.com/regainingperformanceinnetapplications" target="_blank">gave me 100 times performance boost</a>.