With A(1,−2) and B(6,1) fixed, consider all points P(x,y) for which the area of △APB does not exceed 10 square units.
(i) Write the inequality that represents this condition in (x,y).
(ii) Describe geometrically the region in the plane defined by the inequality found in part (i).
(iii) State how the region changes if the inequality symbol ``≤'' is replaced by ``<''.
(iv) Are the points on the line passing through A and B included in the region obtained in part (i)? Give reasons.