### 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:

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 \(OY'\).