Three points X, Y and Z satisfy the following conditions:
• The abscissa of X is positive, and its ordinate is the negative of the abscissa of Y.
• The ordinate of Y is zero.
• The ordinate of Z is positive, and its abscissa equals the sum of the ordinates of X and Y.
Given that ∣abscissa of X∣=5 and ∣ordinate of Z∣=7.
(i) Write all possible coordinate pairs for X, Y and Z that satisfy the above conditions.
(ii) For every set of coordinates obtained, identify the quadrant or axis in which each of the points X, Y and Z lies. Explain your reasoning clearly.
(iii) Out of all the possible sets, choose one set and verify by actual plotting that your quadrant or axis identification is correct.