Exercise 3.1 and 3.2

Q1. How will you describe the position of a table lamp on your study table to another person?

Solution:
Describing the position of a table lamp on your study table to another person (using ideas from coordinate geometry):

1. First, consider the table’s surface as a plane. Imagine choosing one corner of the table as the origin (0, 0).
2. The two edges meeting at that corner represent the x-axis (horizontal edge) and the y-axis (vertical edge).
3. Measure how far the lamp is from the origin along each edge:
   For example, “The lamp is placed 30 cm from the left edge (x-axis) and 20 cm from the front edge (y-axis) of the table.”
4. Thus, the position of the lamp can be described as the point (30, 20) on the table, where 30 cm is the distance along the x-axis and 20 cm is the distance along the y-axis from the origin.

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 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:

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

Solution:

As in the Model of the city plan in Fig-1, It is evident that

1. There is one and only one cross - streets which can be referred to as (4, 3)
2. There is one and only one cross - streets can be referred to as (3, 4).

Write the answer of each of the following questions:

1. What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
2. What is the name of each part of the plane formed by these two lines?
3. Write the name of the point where these two lines intersect.

Solution:

1. \(x\)-Axis and \(y\)-Axis
2. Quadrants
3. Origin

See Fig.3.14, and write the following:

1. The coordinates of B.
2. The coordinates of C.
3. The point identified by the coordinates (–3, –5).
4. The point identified by the coordinates (2, – 4).
5. The abscissa of the point D.
6. The ordinate of the point H.
7. The coordinates of the point L.
8. The coordinates of the point M.

Solution:

1. The coordinates of B.\(\Rightarrow\)(-5,2)
2. The coordinates of C.\(\Rightarrow\)(5,-5)
3. The point identified by the coordinates (–3, –5).\(\Rightarrow\)E
4. The point identified by the coordinates (2, – 4).\(\Rightarrow\)G
5. The abscissa of the point D.\(\Rightarrow\)6
6. The ordinate of the point H.\(\Rightarrow\)-3
7. The coordinates of the point L.\(\Rightarrow\)(0,5)
8. The coordinates of the point M.\(\Rightarrow\)(-3,0)