Three vertices of a rectangle are P(1,2), Q(5,2) and R(5,−1).
(i) Plot the points P,Q and R on a coordinate plane and join them in the given order.
(ii) Determine the coordinates of the fourth vertex S needed to complete rectangle PQRS and justify your answer geometrically.
(iii) Find the coordinates of the point where the diagonals of rectangle PQRS intersect. Give a short explanation for your answer without using any formula beyond what you have studied in Class 9.