The axes create the quadrants.
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None. The coordinate lines between the quadrants don't belong to any of the quadrants.
2-dimensional Cartesian space is naturally split into four quadrants, with one quadrant defined by x>0, y>0; one defined by x<0, y>0; one defined by x<0, y<0; and, one defined by x>0, y<0.
The quadrants formed by the x and y axes are numbered anticlockwise from the quadrant in which both coordinates are positive (which is quadrant I). Thus negative x and positive y is in the quadrant II.
4
infinite number of axes