How to place 4 identical non-overlapping rectangles with corners on 4 randomly preplaced points?

Question

2D Euclidean geometry. I'm not sure if this problem was already asked I tried to search but I failed to find similar. So imagine we have 4 randomly placed points on a plane. And we also have 4 identical rectangles that are "parallel" - i.e. their rotation is the same, for simplicity their long sides are all parallel to x-axis. A rectangle must be placed in such a way that only one of it's corners would touch only one of those 4 points(each rectangle would have it's own point). No 2 rectangles can overlap(but they may touch - e.g. if all 4 points happen to be in the same place). I suspect that we can always place 4 rectangles in this way regardless of where those 4 points are - even if all 4 points are the same point we can put each rectangle to the "north-west","north-east", "south-east" and "south-west" from that point. But I have no proof. And what could be solution(apart from the "try all combinations until you succeed")? So let's have 4 random points: A(Xa, Ya), B(Xb, Yb), C(Xc, Yc), D(Xd, Yd) and we need to determine for each point where would their rectangle be placed relative to the point - NW, NE, SE, SW.