Get 4 points lying on the plane by given normal

Question

I would like to create plane using 4 points (which I need to find out), when I know the intersection point of the 2 diagonals in the plane. Next thing I know, that the Y coord of 2 bottom points will be the same and the top 2 Y coords will be the same.

Basicly I want to create that plane in point O, which is (X, Y) big and allways faces some point in space.

Here is a picture, that hopefuly explains it better:

Answer 1

If you assume that the points form a rectangle, you can see:

$\frac{(P_1+P_3)}{2}=σ $ and $\frac{(P_4+P_2)}{2}=σ $

Moreover if $\vec{n}^{\,}$ is the normal vector of the plane $\implies$ $\forall \vec{v}^{\,} \in \Pi$ $\ $ $v \cdot n=d $

Can you continue from here?