For the convex hull algorithm we have to be able to test whether a point r lies left or right of the directed line through two points p and q. Let p = (px, py), q = (qx, qy), and r = (rx, ry).
a) Show that the sign of the determinant
1 pxpy
D= 1qxqy
1 rxry
determines whether r lies left or right of the line.
b) Show that |D| in fact is twice the area of the triangle determined by p, q, and r.
c) Why is this an attractive way to implement the basic test in algorithm CONVEXHULL? Give an argument for both integer and floating point coordinates.