You are given a set S of n distinct points in the plane in general position (no three points are collinear). The points are specified by their x and y coordinates (real numbers). Prove by construction in as much detail as you can that the set S can be rotated so that no two points lie on a vertical line (have the same x coordinate) 1. 2. Convert your proof into an algorithm (in English - no computer language permitted) that implements your proof. . Provide Big-O, Big-S2, and Big- analyses of the time and space complexities of your algorithm using the Extended real RAM model of computation. You are given a set S of n distinct points in the plane in general position (no three points are collinear). The points are specified by their x and y coordinates (real numbers). Prove by construction in as much detail as you can that the set S can be rotated so that no two points lie on a vertical line (have the same x coordinate) 1. 2. Convert your proof into an algorithm (in English - no computer language permitted) that implements your proof. . Provide Big-O, Big-S2, and Big- analyses of the time and space complexities of your algorithm using the Extended real RAM model of computation