According to the wikipedia,
Although a translation is a non-linear transformation in a 2-D or 3-D Euclidean space described by Cartesian coordinates, it becomes, in a 3-D or 4-D projective space described by homogeneous coordinates, a simple linear transformation (a shear).
I think this is one of the coolest thing I have learned in geometry. Now, I'm wondering who was the first to find it. Thanks!
Well, the first homogeneous coordinates were introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül. However, the coordinates you're interested in, where a point $(x,y)$ is promoted to $(x,y,1)$, were introduced by Julius Plücker in 1831, in the second volume of his Analytisch-geometrische Entwicklungen.
Source: Kline, Mathematical Thought From Ancient to Modern Times, Volume 3, page 853