Six treasure markers are located at the points M1(−6,3), M2(2,5), M3(5,−2), M4(−4,−5), M5(0,4) and M6(−6,−1) on a game map represented by a coordinate plane.
(i) Without plotting, determine which of the markers are collinear with the origin along a line parallel to the y-axis. Explain your reasoning using abscissas and ordinates.
(ii) Starting with the marker having the highest ordinate, list all six markers in the clockwise order around the origin until you return to the starting marker. Provide clear justification for each step in your ordering.
(iii) According to a game rule, a player may visit markers only in increasing order of their abscissas but must finish at the marker with the smallest ordinate. Propose one valid visiting sequence and prove that it satisfies both conditions.