# Introduction

Remember the famous movie “Shashwank Redemption”? In the movie, the protagonist Andy Dufresne (Tim Robbins) tells his prison mate Ellis Boyd (Morgan Freeman) about a letter kept underneath the ground near a tree at a place which was quite far. Andy explains the way to reach at that letter, and Boyd was successfully able to reach at the place. Now think of the same situation in a desert—how would you be able to tell the other person the whereabouts of something that you want him/her to find? We have longitude and latitudes for that. What if I have to show the same on my notebook? Here come the coordinates.So, if I have to denote a point on my notebook, we use two restricting factors—distance from X-axis and distance from Y-axis. What if I have to show a point in the air in my room? Can I show it using only distances from X-axis and Y-axis? Answer is no. My room is a 3-dimensional space, and to be able to show the point in a 3-D space, I need to have three restricting factors—distance from X-axis and distance from Y-axis and distance from Z-axis (or distance from the ceiling), or maybe angle formed by that point from any of the corners of the room.

The method of denoting points with the help of coordinates was proposed by French Mathematician Descartes. Further, he also proposed that lines and curves are nothing but the collection of points, and hence, can be represented by equations derived out of coordinate geometry. To honour his work, the coordinates of a point are often referred to as its Cartesian coordinates.

# Consider the following case

Suppose there is an ant at point O in the figure and it wants to go to point P?

One way to reach P is that the ant travels along OX, reaches A and then travels along AP and reaches P.
Hence, it first covers a distance ‘X’ horizontally and then covers a distance ‘Y’ vertically.
First of all, we will assume a reference point, which is at a distance of 0 unit from both the X-axis and Y-axis and will call this origin.
If we assume ‘O’ as the origin, the distances X and Y are the distances of this point P from Y-axis and X-axis respectively. These are known as coordinates of point P and are written as P(X, Y).