I doubt you want A to be point closest to (0,0), e.g, in the case [1, 100; 2, 0; 1, 200; 2, 200] the closest point to 0 is [2, 0] but I assume you still want A to be [1, 100].
I assume your quadrilateral is convex (otherwise you can make three different simple quadrilaterals with the four points) and you're trying to find the order of the vertices so that they form a simple quadrilateral You can find the order of the vertices from convhull:
Array_1 = [84 113;76 237;108 235;106 115];
order = convhull(Array_1);
assert(numel(order) == 5, 'Points do not form a convex quadrilateral');
orderedpoints = Array_1(order(1:4), :)
orderedpoints will be ordered in counter-clockwise direction, so if you plot them they will always form a simple quadrilateral.
plot(Array_1(order, 1), Array_1(order, 2));
I'm not sure how to work out which of the points is A, but once you've worked it out, you can simply rearrange the points with circshift. E.g if you decide that point 2 in the reordered array is A, then
ptAidx = 2;
ACDB = circshift(orderedpoints, 1-ptAidx, 1)