Cartesian is a coordinate system that specify the position of numbers and vectors in a plane. Cartesian plane may be two dimensional or three dimensional. The axes of system (x-axis, y-axis and z-axis) help to measured to distance.

For Example: if we are given with point (10, 5), it means move 10 units in the x direction(right form the origin) and 5 units towards y direction (upward). A Cartesian coordinate system in a 2D plane has two perpendicular lines (horizontal axis and vertical axis); in 3 D plane, it has three axes (x-axis, y-axis, z-axis). In this section will study about two dimensional Cartesian system, which is defined by an ordered pair of perpendicular axes.

## Graphical Representation

Cartesian system is divided into four quadrants, named as Ist quadrant, 2nd quadrant, 3rd quadrant and 4th quadrant.

Every quadrant has their own rule as mentioned below:

First quadrant: Each coordinate will be positive.

Second quadrant: x coordinate will be negative and y will be positive.

Third quadrant: Both x and y coordinates will be negative.

Fourth quadrant:  x coordinate will be positive and y will be positive negative. This system is used for graphing the numbers as well as vectors. The arrows are used to indicate the infinite length of x axis and y-axis. Both the axes intersect a point called origin (in above image marked as o). Each point can be represented by an ordered pair (x, y), where the y-coordinate is the distance from the x-axis and the x-coordinate is the point's distance from the y axis.

For Example: ordered pair (5, 6) represents a point 5 units to the right of the origin and 6 units upwards from it.

## Examples

Examples on Cartesian representation are given below:
Example 1: For the function y = 5x - 7, set up a table for x and y. Plot all the points on graph.

Solution: Function is y = 5x - 7

Choose the values of x and find the value for y.

Put x = 0 => y = 5 x 0 - 7 = -7

Put x = 1 => y = 5 x 1 - 7 = 3

Put x = 2 => y = 5 x 2 - 7 = 13

Put x = -1 => y = 5 x -1 - 7 = -17

 x y 0 -7 1 -2 2 3 -1 -12 Example 2: Find the which quadrant of the coordinate system Points are P(10, -4), Q(6,10) and R(-2, 3).

Solution: Plot all the given points in the coordinate system. From the above diagram:

P(10, -4) is lies in fourth quadrant.

Q(6,10) is lies in first quadrant and

R(-2, 3) is lies in second quadrant.