For the triangle ABC with vertices A(-4,1), B(b,7) and C(2,-5), answer the following:
(i) Derive an expression for the area of the triangle in terms of the unknown coordinate b.
(ii) Using your result from part (i), determine the possible numerical values of b when the area is 30 square units.
(iii) Give a brief geometrical explanation for the existence of two distinct values of b in part (ii).