A rectangular playground has its vertices at P(1,2), Q(1,8), R(9,8) and S(9,2) in the coordinate plane.
a. (i) Calculate the length of the diagonal PR.
b. (ii) Write the value of (PR)2 without evaluating the square root.
c. (iii) A drinking-water tap is to be fixed exactly at the midpoint of side QR. Determine the coordinates of this point.