Ex - 3.1
Question 1. How will you describe the position of a table lamp on study table to another person?
Solution
There are many cross-streets in your model. A particular cross-street is made by two streets, on running in the North-South direction and another in the East-West direction. Each cross street is referred to in 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).
Question 1. How will you describe the position of a table lamp on study table to another person?
Solution
Consider that the lamp is placed on the table. Here two references must be used to ascertain the position. Choose two adjacent edges DC and AD. Now draw perpendiculars on the two edges from the position of lamp and measure the lengths of these perpendiculars. Let the length of these perpendiculars be 30 cm and 25 cm respectively. Now the position of the lamp from the left edge (AD) is 25 cm and from the lower edge (DC) is 30 cm. Then the position of the table will be given by the points (25, 30).
Concept Insight: Since there are two dimensions length and breadth of the table so two references are required to ascertain the position on the table. The point where the two edges of table can be taken as the references In this case we can have origin at any of the four corners. The perpendicular distance from the edges will give the position of lamp. Remember that (25, 30) and (30, 25) represent two different positions on the table.
Question 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 about 5 streets in each direction. Using 1 cm = 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, on running in the North-South direction and another in the East-West direction. Each cross street is referred to in 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
Both the cross- streets are marked in the above figure. We may observe that there is only one cross street which can be referred as (4, 3) and also only one which can be referred as (3, 4).
Concept Insight: Consider north-south and west-east directions as two perpendicular axes. The point where the two axes intersect is called the origin. Drawing line parallel to x axis and y axis will give the five streets for each of the two given directions. Any point (x,y) on Cartesian plane represents a distance of x units from y axis and y units from x axis. Coordinate points (x,y) and (y,x) represents two different positions on a plane if 
. Each coordinate point on the Cartesian plane determines a unique position.
. Each coordinate point on the Cartesian plane determines a unique position.
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