The points A(k, −3), B(4, 2) and C(−1, 5) form a triangle for real values of k.
(i) Obtain an algebraic expression in k whose sign decides the orientation (clockwise or counter-clockwise) of triangle ABC when the vertices are read in the order A, B, C.
(ii) Hence determine all real values of k that make the order A, B, C clockwise.
(iii) For k = 7, calculate the area of triangle ABC and state its orientation.