1. How will you describe the position of a table lamp on your study table to another person?
To describe the position of a table lamp on a study table to someone else, you can use a coordinate system:
Imagine the surface of the study table as a flat plane divided into two axes:
The X-axis (horizontal line) represents the breadth of the table.
The Y-axis (perpendicular line) represents the length of the table.
Choose one corner of the table as the origin (0, 0) where the X-axis and Y-axis meet.
To locate the table lamp, draw an imaginary line from the origin to the lamp’s position.
Measure the distance from the lamp to the X-axis (breadth-wise) and the Y-axis (length-wise).
These measurements give the coordinates of the table lamp.
For example, if the distance from the lamp to the X-axis is 15 units and to the Y-axis is 25 units, the position of the lamp in coordinate form is (15, 25).
Thus, the position of the table lamp on the study table is represented as (15, 25) in this coordinate
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 in 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 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)?
- Only one street can be referred to as (4,3) (as clear from the figure).
- Only one street can be referred to as (3,4) (as we see from the figure).
3.Write the answer to each of the following questions.
(i) What is the name of the horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane?
(ii) What is the name of each part of the plane formed by these two lines?
(iii) Write the name of the point where these two lines intersect.
Solution:
(i) The name of horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane is the x-axis and the y-axis, respectively.
(ii) The name of each part of the plane formed by these two lines, the x-axis and the y-axis, is quadrants.
(iii) The point where these two lines intersect is called the origin.