### Theory:

The $$x$$ - axis and $$y$$ - axis divide the cartesian plane into four regions from the origin. These are called quadrants. They are usually numbered in anticlockwise direction starting from the region bounded by positive $$x$$ and $$y$$ axis (that is $$OX$$).

Quadrant I:
• Any point located in quadrant $$I$$ will have a positive number in the $$x$$ - axis and $$y$$ - axis.
• That is, $$x > 0$$, $$y > 0$$.
• The region is $$XOY$$.
Example:
$$(2,3)$$, $$(6,10)$$, $$(9,12)$$
Quadrant II:
• Any point located in quadrant $$II$$ will have a negative number in the $$x$$ - axis and a  positive number in $$y$$ - axis.
• That is, $$x < 0$$, $$y > 0$$.
• The region is $$X'OY$$.
Example:
$$(-3,6)$$, $$(-2,5)$$, $$(-15,12)$$
Quadrant III:
• Any point located in quadrant $$III$$ will have a negative number in the $$x$$ - axis and $$y$$ - axis.
• That is, $$x < 0$$, $$y < 0$$.
• The region is $$X'OY'$$.
Example:
$$(-5,-6)$$, $$(-2,-1)$$, $$(-8,-10)$$
Quadrant IV:
• Any point located in quadrant $$IV$$ will have a positive number in the $$x$$ - axis and a negative number in $$y$$ - axis.
• That is, $$x > 0$$, $$y < 0$$.
• The region is $$XOY'$$.
Example:
$$(1,-3)$$, $$(3, -4)$$, $$(7,-1)$$ Coordinate of a point on the axes:
• If a point lies on the $$x$$ - axis, then the coordinate is $$(x,0)$$. That is, $$y=0$$.
Example:
$$(-3,0)$$, $$(6,0)$$, $$(1,0)$$.
• If a point lies on the $$y$$ - axis, then the coordinate is $$(0,y)$$. That is, $$x=0$$.
Example:
$$(0,-1)$$, $$(0,5)$$, $$(0,10)$$.