Chapter 3: Coordinate Geometry

EXERCISE 3.1

1. How will you describe the position of a table lamp on your study table to another person ?

Solution:  Consider the lamp as a point and table as a plane . Choose any two perpendicular edges of the table . Measure the distance of the lamp from the longer edge, suppose it is 15 cm . Again, measure the distance of the lamp from the shorter edge , and suppose it is 25 cm . We can write the position of the lamps as (15,25) , depending on the order you fix .

2. (Street plan) : A city has two main roads which cross each other at the centre of the city . These two roads are along the North-South direction and East – West direction .

All the other streets of the city run parallel to these roads and are 200 m apart .there are 5 streets in each direction . Using 1cm = 200 m , draw a model of the city  on your notebook . Represent the roads/streets by single lines .

There are many cross-streets in your model . A particular cross-street is made by two streets , one running in the North-South direction and another in the East-West direction . Each cross streets is referred to the following manner : If the 2nd street running in the North –South direction and 5th in the East-West direction meet at some crossing , then we will call this cross-street (2 , 5) . Using this convention , find :  (i) how many cross-streets can be referred to as (4 ,3) 

                                  (ii) how many cross-streets can be referred to as (3 , 4) .

Solution : The street plan is shown in figure given below .

Both the cross-streets are marked street plan figure .   

(i) The street 4 and street 3 are both the cross-streets can be referred to as (4 ,3) .

(ii) The street 3 and street 4 are both the cross-streets can be referred to as (3 ,4) .

The two cross-streets are uniquely found because of the two reference lines we have used for locating them .