Translation

This is not the question of translating the gibberish language of math into english, but rather that of moving the vector end-point to a new position relative to its current position. Translating all the points in a 3D-figure the same length would constitute moving the entire object in space by that amount.

Unfortunately, this translation can not be represented by a multiplication as we wish: Y=MX, where Y and X are vectors and M is the transformational matrix. What we do to solve this is add another dimension. This might seem like an unneccesary thing to do, since we have too many dimensions to begin with, but this solves the problem of representing the translation as a matrix multiplication.

In this new four-dimensional world, the fourth dimension is used merely as a dummy to allow for simple multiplications. Each vector in 3D can be mapped onto a vector in 4D such that u=(x,y,z)=>v=(x,y,z,1).

Such a coordinate is a homogenous coordinate. Likewise there are homogenous matrices that can be written like this: