### Theory:

Number line:

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:

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 $$(0,0)$$.

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.
{\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 $$OY'$$.