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.

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.

Graphical Representation

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 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
-7
1
-2
 2  3
 -1  -12

Cartesian Representation Graph

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.

Cartesian Representation Graph Examples
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.