Let a,b,c,d be positive real numbers.
Three points are defined as follows:
P(a,−b), Q(−c,−d) and R(0,d).
(i) For each point, state the quadrant or axis on which it lies.
(ii) If a=d and b=c, determine whether any two of the three points can lie in the same quadrant or on the same axis. Give a reason for each conclusion.
(iii) Suppose b=0. Describe completely the set of possible positions of the modified point P(a,0) and explain how its location differs from that of R.