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Cartesian System

Although we have learnt to locate a point on a number line we should learn to describe the position of a point. This will have to be done with reference to more than one line. To understand this concept let us visualize the following situation:

Students from classes 1 to 10 ( each of class strength =30 ) are requested to stand for the assembly in the following manner:

Each class forms two rows thus, there being (2´ 15) =30 rows in all.

Roll numbers of each class from 1-15 form the first row of their Class and Roll numbers from 16-30 occupy the next of their respective class.

Each student is asked to stand equidistance from each other in the row or amongst two rows.

The standing arrangement of the students will be as follows:


How to locate a boy, he is in third standard whose Roll number is 20, is indicated by the above visual.

Using the same arrangement we could locate the position of any student knowing her Class and Roll number.

From the above discussions we understand that the position of any object in a plane can be represented with the help of two perpendicular lines, as in the above discussion when we talk about the number of the row and that of the column. This same rule is applied in the case of the position of a point on a paper (we require the distance from the bottom of the page as well as the distance from left side of the paper). Also, we use the same to find the position of a student in a certain seating arrangement (we require the number of the row and that of the column). This simple idea has given rise to a very important Branch of Mathematics called Co-ordinate Geometry. Let us look at some basic concepts of this branch of Mathematics:

The horizontal line is usually called x-axis and the vertical line is usually called y-axis. The point of intersection of these two axes is called the origin and is labelled O on each number line. The coordinates of the origin are (0, 0).

The axes divide the plane into four parts called quadrants.
In first quadrant both x and y are positive; second quadrant x is negative and y is positive; the third quadrant both are negative; the fourth quadrant x is positive and y is negative.
The plane itself is called the Co-ordinate plane or the Cartesian plane or xy-plane.


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