Why are Homogeneous Coordinates used in Computer Graphics? Why are Homogeneous Coordinates used in Computer Graphics?

What would be the problem if Homogeneous Coordinates were not used in matrix transformations?
They simplify and unify the mathematics used in graphics:


They allow you to represent translations with matrices.
They allow you to represent the division by depth in perspective projections.


The first one is related to affine geometry.
The second one is related to projective geometry.