How to obtain an n-sided polygon's plane equation from the co-ordinates of the n vertices?

Question

We are given n co-ordinates like so: (x1, y1), (x2, y2),.....,(xn, yn). The points will form a polygon when connected. The shape of the polygon could be anything (symmetric or non-symmetric). If we consider the polygon to be a 2D plane, in this case, how can we obtain the plane equation of the polygon formed from only the given co-ordinates? The z-coordinate value will always remain zero.