# Cartesian System

## Cartesian plane & Coordinate Axes

**Cartesian Plane**: A cartesian plane is defined by **two perpendicular number lines**, A horizontal line(x−axis) and a vertical line (y−axis).

These lines are called coordinate axes. (Cartesian plane is named after French mathematician **Rene Descartes**, who formalized its use in mathematics) The Cartesian plane extends infinitely in all directions.

**Origin**: The coordinate axes intersect each other at right angles, **The point of intersection** of these two axes is called Origin.

Two perpendicular number lines intersecting at point zero are called **coordinate axes**. The horizontal number line is the ** x-axis** (denoted by

*X’OX*) and the vertical one is the

**(denoted by**

*y*-axis*Y’OY*). The point of intersection of

*x-*axis and

*y-*axis is called

**origin**and denoted by ‘

*O*’.

**Cartesian plane** is a plane obtained by putting the coordinate axes perpendicular to each other in the plane. It is also called coordinate plane or *xy* plane.

The **x-coordinate** of a point is its perpendicular distance from *y-*axis.

The **y-coordinate** of a point is its perpendicular distance from *x-*axis.

The point where the *x *axis and the *y *axis intersect is represented by coordinate points (0, 0) and is called the **origin**.

## Quadrants

The cartesian plane is divided into four equal parts, called **quadrants. **These are named in order as I,II,III and IV starting with the upper right and going around in anticlockwise direction.

The **abscissa** of a point is the *x*-coordinate of the point. The **ordinate** of a point is the *y-*coordinate of the point.

If the abscissa of a point is *x* and the ordinate of the point is *y*, then (*x, y*) are called the **coordinates** of the point.

The axes divide the Cartesian plane into four parts called the **quadrants** (one fourth part), numbered I, II, III and IV anticlockwise from *OX*.

Sign of coordinates depicts the quadrant in which it lies. The coordinates of a point are of the form (+, +) in the first quadrant, (-, +) in the second quadrant, (-,-) in the third quadrant and (+,-) in the fourth quadrant.

The coordinates of a point on the *x*-axis are of the form (*x*, 0) and that of the point on *y*-axis are (0, *y*).

To plot a point P (3, 4) in the Cartesian plane, start from origin and count 3 units on the positive *x* axis then move 4 units towards positive *y* axis. The point at which we will arrive will be the point *P* (3, 4).

*Quadrants *

**Points in different Quadrants.**

**Signs of coordinates of points in different quadrants:**

**Quadrant:**‘+’ x – coordinate and ‘+’ y – coordinate. E.g. (2,3)**Quadrant:**‘-’ x – coordinate and ‘+’ y – coordinate. E.g. (-1,4)**Quadrant:**‘-’ x – coordinate and ‘-’ y – coordinate. E.g. (-3,-5)**Quadrant:**‘+’ x – coordinate and ‘-’ y – coordinate. E.g. (6,-1)

# Plotting on a Graph

## Representation of a point on Cartesian plane

Using the co-ordinate axes, we can describe any point in the plane using an ordered pair of numbers. A point **A **is represented by an ordered pair (x,y) where, x is the **abscissa** and y is the **ordinate** of the point.

*Position of a point in a plane*

## Plotting a point

The location of a point in the plane is given by its coordinates,the first number x gives the point’s horizontal position and the second number y gives its vertical position.

For example, Point (3,2) is 3 units away from positive y-axis and 2 units away from positive x-axis.

Therefore, point (3,2) can be plotted as shown below. Similarly, (-2,3), (-1,-2) and (2,-3) are plotted.

*Plotting a point in the plane*