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.
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The axes create the quadrants.
None. The coordinate lines between the quadrants don't belong to any of the quadrants.
In math, Q1 refers to the first quadrant of a graph (which has a total of four quadrants), or the quadrant in the upper right hand corner. It contains both positive x and y values. This is especially useful in trigonometry when visualizing the sin(x) cos(x) and tan(x) functions.
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Quadrants I and III. In Quadrant I, the values are both positive. In Quadrant III, the values are both negative.