Introduction

You have already studied how to locate a point on a number line. You also know how to describe the position of a point on the line. There are many other situations, in which to find a point we are required to describe its position with reference to more than oneone line.

For example, consider the following situations:

Not as easily as when we know two pieces of information about it, namely, the number of the street on which it is situated, and the house number.

If we want to reach the house which is situated in the 2nd street and has the number 5, first of all we would identify the 2nd street and then the house numbered 5 on it.

In the above figure, H shows the location of the house. Similarly, P shows the location of the house corresponding to Street number 74 and House number 47.

II. Suppose you put a dot on a sheet of paper. If we ask you to tell us the position of the dot on the paper, how will you do this? Perhaps you will try in some such manner: “The dot is in the upper half of the paper”, or “It is near the left edge of the paper”, or “It is very near the left hand upper corner of the sheet”.

Do any of these statements fix the position of the dot precisely? NoYes!

But, if you say “ The dot is nearly 5 cm away from the left edge of the paper”, it helps to give some idea but still does not fix the position of the dot. A little thought might enable you to say that the dot is also at a distance of 9 cm above the bottom line. We now know exactly where the dot is!

For this purpose, we fixed the position of the dot by specifying its distances from two fixed lines, the left edge of the paper and the bottom line of the paper. In other words, we need two independent informations for finding the position of the dot. Now, perform the following classroom activity known as ‘Seating Plan’.

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Activity 1 (Seating Plan) :

Draw a plan of the seating in your classroom, pushing all the desks together. Represent each desk by a square. In each square, write the name of the student occupying the desk, which the square represents. Position of each student in the classroom is described precisely by using two independent informations:

(i) the column in which she or he sits.

(ii) the row in which she or he sits.

If you are sitting on the desk lying in the 5th column and 3rd row (represented by the shaded square in Fig. 3.3), and we write the column first and then the row second: your position could be written as (5,3)(3,5).

What if we choose to write the row number first and then the column number i.e. (3,5)(5,3).

Is this the same as (5, 3)? NoYes

Write down the names and positions of other students in your class. For example: if Sonia is sitting in the 4th column and 1st row, write S(4,1). The teacher’s desk is not part of your seating plan. We are treating the teacher just as an observer.

In the discussion above, you observe that position of any object lying in a plane can be represented with the help of two perpendicular lines. In case of ‘dot’, we require distance of the dot from bottom line as well as from left edge of the paper.

In case of seating plan, we require the number of the column and that of the row. This simple idea has far reaching consequences, and has given rise to a very important branch of Mathematics known as Coordinate Geometry. In this chapter, we aim to introduce some basic concepts of coordinate geometry. You will study more about these in your higher classes. This study was initially developed by the French philosopher and mathematician René Déscartes.

René Déscartes, the great French mathematician of the seventeenth century, liked to lie in bed and think! One day, when resting in bed, he solved the problem of describing the position of a point in a plane. His method was a development of the older idea of latitude and longitude. In honour of Déscartes, the system used for describing the position of a point in a plane is also known as the Cartesian system.