Why do 2D transformations need 3x3 matrices?

Question

I want to do some 2D drawing and thus want to implement some matrix transformations. With my light mathematics background I am trying to understand how to do so in C# (any o

Answer 1

The answer is Homogeneous Coordinates. To combine rotation and translation in one operation one extra dimension is needed than the model requires. For planar things this is 3 components and for spatial things this is 4 components. The operators take 3 components and return 3 components requiring 3x3 matrices.