Coordinate System

Cartesian coordinates are defined through the use of two coordinate lines, one horizontal and the other vertical.


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Let their point of intersection be $$O$$, which we call the origin, and the real number $$0$$ of both lines is represented by $$O$$. The two lines are called the coordinate axes. The horizontal line $$X’OX$$ is called the X–Axis and the vertical line $$Y’OY$$ is called the Y–Axis.

A point is indicated by giving its distance and direction using the coordinate axes. The line segment from the Y–Axis to the point and parallel to X–Axis is called the abscissa of the point and the line segment from the X–Axis to the point and parallel to the Y–Axis is called the ordinate. These two distances are referred to as the coordinates of the point. The ordinate of every point on the X–Axis is zero, the abscissa of every point on the Y–Axis is zero and the coordinates of the origin are both zero.

The coordinate axes divide the plane into four equal parts called quadrants. They are defined as follows:


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Quadrant 1:
All points $$\left( {x,y} \right)$$ with $$x > 0,\,y > 0$$.
Quadrant 2:
All points $$\left( {x,y} \right)$$ with $$x < 0,\,y > 0$$.
Quadrant 3:
All points $$\left( {x,y} \right)$$ with $$x < 0,\,y < 0$$.
Quadrant 4:
All points $$\left( {x,y} \right)$$ with $$x > 0,\,y < 0$$.