Consider a seating plan of students in an auditorium. Push all the seats together and represent each seat with a square. Each square describe the position of each student with two independent information
a) The row in which he/she sits.
b) The column in which he/she sits.
Now, if the student 'A' is sitting in the third row and the fifth column. find the position of his friend sitting two columns away(to A's right-hand side).
It requires two number lines
You already have studied how to locate a point on a number line. If the students were sitting only horizontally in a single row, it would have been easy to locate the position of the friend.
The circle in the fifth column and the third row indicates the reference point (student A) and now, we have to find a friend which is two columns away, i.e., the third column as shown in the figure.
Finding the position, when there are rows and columns, requires the aid of two number lines, one horizontal and the other, vertical.
This very important concept of using two number lines, discovered by Rene Descartes, is known as the Cartesian system.