Non Self Intersecting Polygons?

Question

Given a set of n points is it always possible to construct a non self intersecting polygon?

Answer 1

Choose a point $x_0$ of your set and order the other points around $x_0$ counter-clockwise. Label them $x_1,x_2,\ldots x_{n-1}$ according to that order. You get a non intersecting polygon and $x_0$ is in its kernel.