Let D(−2, 1), E(3, 6) and F(8, 1) be three distinct points in the plane.
(a) Prove that the points D, E and F are non-collinear without using distance formula.
(b) Compute the signed area when the vertices are written in the order F, E, D and state whether this ordering is clockwise or counter-clockwise.
(c) Interchange any two vertices of part (b) and show that the sign of the signed area obtained in part (b) changes, thereby confirming the relation between sign and orientation.