4: suppose nine distinct points in p2(c) are given and that they are not all collinear. suppose that any straight line that passes through two of these points also passes through a third 1. show that there is a projectivity taking these points to [0: 1: -1] (–1: 0: 1] [0: 1: a] [a : 0: 1] [0 : a : 1] (1: 0: a] [1: -1: 0) [1: a: 0) [a: 1: 0) for some a ec. 2. show that a2 - a+1=0. 3. show that a projective cubic passes through the nine points above if and only if it is defined by an equation of the form a(x3 + y3 + 73) +bxyz = 0 for some ſa : b] e pl(c). (hint: view the space of projective cubics as p(c[x, y,