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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 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.

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 that is mapped (projected) to a 2-dimensional point in the Euclidean plane: $(x/w, y/w).$ Given that, $(x,y,1)$ would be 2-dimensional plane in that 3-dimensional space (or a specific point if $x$ and $y$ are fixed) that maps to $(x,y)$ in the standard Euclidean 2-dimensional plane.

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. 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.

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 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.

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 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.

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. 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.