Cartesian Co-ordinate System – Brief History & Introduction

Rene Descartes, a great French mathematician and Philosopher of 17th Century did a ground breaking work in the field of Analytical Geometry or Cartesian Geometry.

The story goes that, once while he was lying in bed and he observed a fly on the ceiling. He started thinking to describe the location of the fly using the square tiles of the ceiling. He thought, if he had a starting point, he could find both the number of squares over and up. This is how he could describe the exact location of the fly.

Thus the rectangular co-ordinate system also called Cartesian Co-ordinate system after Descartes name, was discovered.

In this system each point in a two dimensional plane can be expressed by two numbers, one of which gives the horizontal location and the other which gives the vertical location and we call these numbers as Cartesian Co-ordinates.

He used two perpendicular lines (horizontal known as x-axis and vertical known as y-axis) intersecting each other at a point called origin to measure the horizontal distance called abscissa (or x) and vertical distance called ordinate (or y).

He is also known as ‘Father of Modern Philosophy’, one of his famous quotes is:

“I think, therefore I am”

Descartes used analytical tools of algebra in geometry. Which enabled to solve a pair of simultaneous equations either algebraically or graphically. Which provided platform for the development of Newton’s and Leibniz’s Calculus.

In Cartesian Co-ordinates System the x and y – axis divides the plane into four quadrant I, II, III and IV. The signs of x and y co-ordinates in each quadrant are given in the following table:

y co-ordinate of each point on x-axis is 0 and x co-ordinate of each point on y-axis  is 0. Which means a point on x-axis is of the form: (a, 0) and each point on y-axis is of the form (0, b).