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.