The problem is as follows. Four masses of $1$ $kg$, $2$ $kg$, $3$ $kg$, and $4$ $kg$ are arranged in square shape. The side length of the square is $1$ $m$. Find the location of the center of mass of this system.
I have found the solution to it to be ($1/2$, $3/10$) by representing the masses as points on the cortisone plane like here. However in the calculations, $4$ $kg$ is always multiplied by zero, so that made me wonder if the center of mass is the same even if the fourth object is $1000$ $kg$. Why is that?