Lesson: Coordinate Geometry

Exercise: 3.1 (2)

Question: 1

How will you describe the position of a table lamp on

your study table to another person?

Solution:

To locate the position of a lamp on a study table, let’s

assume the table as a plane.

Let’s consider one corner of the table as the origin.

Now, let’s take two lines, a perpendicular and a

horizontal. The perpendicular line can be the y-axis

and the horizontal line can be the x-axis. Now, the

length of the table is y-axis and the breadth is the

x-axis.

From the origin, we join a line to the lamp and mark a

point. To find the position of this point, we need to

find the distance of this point from both x-axis and y-

axis and write it in terms of coordinates.

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 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 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) Only one cross street can be referred to as (4, 3)

as shown in the figure.

(ii) Only one cross street can be referred to as (3, 4)

as shown in the figure.

Exercise 3.2 (2)

Question: 1

Write the answer of each of the following questions:

(i) What are the names of the horizontal line and the

vertical line that help 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 names of the horizontal line and the vertical

line are x-axis and y-axis, respectively.

(ii) The name of each part of the plane formed by

these two lines is a quadrant.

(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 coordinates of B are (−5, 2).

(ii) The coordinates of C are (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 the x-coordinate of a point. So, the

abscissa of the point D is 6.

(vi) Ordinate means the y-coordinate of a point. So,

the ordinate of the point H is −3.

(vii) The coordinates of the point L are (0, 5).

(viii) The coordinates of the point M are (−3, 0).

Exercise 3.3 (2)

Question: 1

In which quadrant or on which axis do each of the

points (−2, 4), (3, −1), (−1, 0), (1, 2) and (−3, −5)

lie? Verify your answer by locating them on the

Cartesian plane.

Solution:

(−2, 4) → Second quadrant

(3, −1) → Fourth quadrant

(−1, 0) → x-axis

(1, 2) → First quadrant

(−3, −5) → Third quadrant

Question: 2

Plot the points (x, y) given in the following table on

the plane, choosing suitable units of distance on the

axes.

x

−2

−1

0

1

3

Y

8

7

−1.25

3

−1

Solution

We have consider 1 unit = 1 cm.