# Project a Square as rectangle in projection plane using perspective projection

Consider a square S with vertices (1,1,0), (1,-1,0), (-1,-1,0) and (-1,1,0) and a plane P defined by $$z=1$$. Let the perspective projection of S on P is denoted by S'. What coordinates of the Center of projection(COP) will convert the square S in rectangle or rhombus in S'?

I found this question in my class test. As the object and the projection plane are parallel to each other, i think every coordinates for center of projection will generate square. But i can't find any valid mathematical proof for that. Is my assumption valid or not?