I suppose in some respects it's a matter of perspective (no pun intended).  The ordered triple $(x,y,w)$ is a point in a 3-dimensional [projective space][1]. Projective space that is mapped (projected) to a 2-dimensional point in the Euclidean plane: $(x/w, y/w).$  Given that, $(x,y,1)$ would be point in that 3-dimensional space that maps to the point $(x,y)$ in a 2-dimensional plane.


  [1]: https://en.wikipedia.org/wiki/Projective_space