## Ex 3.1

**Question 1.**

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

Solution:

To describe the position of a table lamp placed on the table, let us consider the table lamp as P and the table as a plane.

Now choose two perpendicular edges of the table as the axes OX and OY.

Measure the perpendicular distance ‘a’cm of P (lamp) from OY. Measure the perpendicular distance ‘b’ cm of P (lamp) from OX.

Thus, the position of the table lamp P is described by the ordered pair (a, b).

**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 other streets of the city run parallel to these roads and are 200 m apart. There are 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, 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 2^{nd} street running in the North-South direction and 5^{th} 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:

(i) A unique cross street as shown by the point A(4, 3).

(ii) A unique cross street as shown by the point B(3,4).

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

## Ex 3.2

**Question 1.**

**Write the answer of each of the following questions:**

**(i) What is the name of horizontal and the 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 x-axis and y-axis respectively.

(ii) The name of each part of the plane formed by these two lines x-axis and y-axis is quadrants.

(iii) The point where these two lines intersect is called the origin.

**Question 2.**

**See Fig.3.14, and write the following:**

**i. The coordinates of B.**

**ii. The coordinates of C.**

**iii. The point identified by the coordinates (–3, –5).**

**iv. The point identified by the coordinates (2, – 4).**

**v. The abscissa of the point D.**

**vi. The ordinate of the point H.**

**vii. The coordinates of the point L.**

**viii. The coordinates of the point M.**

Solution:

i. The co-ordinates of B is (−5, 2).

ii. The co-ordinates of C is (5, −5).

iii. The point identified by the coordinates (−3, −5) is E.

iv. The point identified by the coordinates (2, −4) is G.

v. Abscissa means x co-ordinate of point D. So, abscissa of the point D is 6.

vi. Ordinate means y coordinate of point H. So, ordinate of point H is -3.

vii. The co-ordinates of the point L is (0, 5).

viii. The co-ordinates of the point M is (−3, 0).

## Ex 3.3

**Question 1.**

**Question 2.**

The points to plotted on the (x, y) are:

i. (-2, 8)

ii. (-1, 7)

iii. (0, -1.25)

iv. (1, 3)

v. (3, -1)

On the graph mark X-axis and Y-axis. Mark the meeting point as O.

Now, Let 1 unit = 1 cm