Theory:

Number line:
 
3 (1).png
 
In the above number line, the position of point \(P\) in the above line can be represented as \(6\) units with reference to one line (horizontal line).
 
A similar rule applies to the negative side of the number line as well. It is possible to represent the position of a point with reference to more than one point.
 
Descartes invented placing two such number lines perpendicular to each other on a plane and locating points on the plane by referring them to these lines. The perpendicular lines may be in any direction. But, when we choose these two lines to locate a point in a plane in this chapter, one line will be horizontal(First image) and the other will be vertical(Second image), as below:
 
1259_3_1.png
 
1259_1_1.png
 
Let us combine these \(2\) lines in such a way they are perpendicular to each other. These two lines intersect each other at the point \((0,0)\).
 
1259_4.png
 
Cartesian system:
  • It is a co-ordinate number system used to describe the position of a point in two dimensions by means of two perpendicular lines (x axis and y axis).
  • The line \(X'OX\) is the horizontal line called the \(x\) - axis.
  • The line \(Y'OY\) is the vertical line called the \(y\) - axis.
Co-ordinate axes:
The plural form of the axis is called the axes. A number line represented horizontally is the \(x\) - axis, and a number line represented vertically is the \(y\) - axis. Joining both the lines together at origin is called the \(xy\) plane or cartesian plane or co-ordinate axes.
1259_5.png
{\color{Red} Sample}
Signs in the graphs:
  • In \(x\) - axis, the point is positive along the direction \(OX\) and negative along the direction \(OX'\).
  • In \(y\) - axis, the point is positive along the direction \(OY\) and negative along the direction \(OY'\).