Three vertices of a rectangle are P(1,2), Q(1,−3) and R(5,−3).
(i) Plot these three points on a Cartesian plane.
(ii) Determine the coordinates of the fourth vertex S so that PQRS is a rectangle with sides parallel to the axes. Explain your reasoning.
(iii) State the quadrant in which each vertex of the rectangle lies.
(iv) Without using any formula other than counting squares, find the length of each side of the rectangle.