# Introduction to Graphs - Exercise 27.1 Notes | Study Mathematics (Maths) Class 8 - Class 8

## Class 8: Introduction to Graphs - Exercise 27.1 Notes | Study Mathematics (Maths) Class 8 - Class 8

The document Introduction to Graphs - Exercise 27.1 Notes | Study Mathematics (Maths) Class 8 - Class 8 is a part of the Class 8 Course Mathematics (Maths) Class 8.
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1. Plot the points (5, 0), (5, 1), (5, 8). Do they lie on a line? What is your observation?
Solution:
Take a point O on the graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on the x-axis and y-axis 1 cm represents 1 unit.
To plot point (5, 0), we start from the origin O and move 5 cm along X - axis. The point
we arrive at is point (5, 0).
To plot point (5, 1), we move 5 cm along X - axis and 1 cm along Y - axis. The point we
arrive at is point (5, 1).
To plot point (5, 8), we move 5 cm along X - axis and 8 cm along Y - axis. The point we
arrive at is point (5, 8).

From the above graph, we observe that all points are having same X – coordinates, it can
be seen that the points lie on a line parallel to the y-axis. Hence all points lie on the same
line.

2. Plot the points (2, 8), (7, 8) and (12, 8). Join these points in pairs. Do they lie on a
line? What do you observe?
Solution:

Take a point O on the graph paper and draw the horizontal and vertical lines OX and OY
Page 2

1. Plot the points (5, 0), (5, 1), (5, 8). Do they lie on a line? What is your observation?
Solution:
Take a point O on the graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on the x-axis and y-axis 1 cm represents 1 unit.
To plot point (5, 0), we start from the origin O and move 5 cm along X - axis. The point
we arrive at is point (5, 0).
To plot point (5, 1), we move 5 cm along X - axis and 1 cm along Y - axis. The point we
arrive at is point (5, 1).
To plot point (5, 8), we move 5 cm along X - axis and 8 cm along Y - axis. The point we
arrive at is point (5, 8).

From the above graph, we observe that all points are having same X – coordinates, it can
be seen that the points lie on a line parallel to the y-axis. Hence all points lie on the same
line.

2. Plot the points (2, 8), (7, 8) and (12, 8). Join these points in pairs. Do they lie on a
line? What do you observe?
Solution:

Take a point O on the graph paper and draw the horizontal and vertical lines OX and OY

respectively.
Then, let on the x-axis and y axis 1 cm represents 1 unit.
In order to plot point (2, 8), we start from the origin O and move 8 cm along X - axis. The
point we arrive at is (2, 8).
To plot point (7, 8), we move 7 cm along X - axis and 8 cm along Y - axis. The point we
arrive at is (7, 8).
To plot point (12, 8), we move 12 cm along X - axis and 8 cm along Y - axis. The point
we arrive at is (12, 8).

From the above graph, we observe that all points are having same Y – coordinates, it can
be seen that the points lie on a line parallel to the x-axis. Hence all points lie on the same
line.

3. Locate the points :
(i) (1, 1), (1, 2), (1, 3), (1, 4)
(ii) (2, 1), (2, 2), (2, 3), (2, 4)
(iii) (1, 3), (2, 3), (3, 3), (4, 3)
(iv) (1, 4), (2, 4), (3, 4), (4, 4,)
Solution:
(i) (1, 1), (1, 2), (1, 3), (1, 4)
To plot these points,
Take a point O on a graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on x-axis and y-axis 1 cm represents 1 unit.
Page 3

1. Plot the points (5, 0), (5, 1), (5, 8). Do they lie on a line? What is your observation?
Solution:
Take a point O on the graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on the x-axis and y-axis 1 cm represents 1 unit.
To plot point (5, 0), we start from the origin O and move 5 cm along X - axis. The point
we arrive at is point (5, 0).
To plot point (5, 1), we move 5 cm along X - axis and 1 cm along Y - axis. The point we
arrive at is point (5, 1).
To plot point (5, 8), we move 5 cm along X - axis and 8 cm along Y - axis. The point we
arrive at is point (5, 8).

From the above graph, we observe that all points are having same X – coordinates, it can
be seen that the points lie on a line parallel to the y-axis. Hence all points lie on the same
line.

2. Plot the points (2, 8), (7, 8) and (12, 8). Join these points in pairs. Do they lie on a
line? What do you observe?
Solution:

Take a point O on the graph paper and draw the horizontal and vertical lines OX and OY

respectively.
Then, let on the x-axis and y axis 1 cm represents 1 unit.
In order to plot point (2, 8), we start from the origin O and move 8 cm along X - axis. The
point we arrive at is (2, 8).
To plot point (7, 8), we move 7 cm along X - axis and 8 cm along Y - axis. The point we
arrive at is (7, 8).
To plot point (12, 8), we move 12 cm along X - axis and 8 cm along Y - axis. The point
we arrive at is (12, 8).

From the above graph, we observe that all points are having same Y – coordinates, it can
be seen that the points lie on a line parallel to the x-axis. Hence all points lie on the same
line.

3. Locate the points :
(i) (1, 1), (1, 2), (1, 3), (1, 4)
(ii) (2, 1), (2, 2), (2, 3), (2, 4)
(iii) (1, 3), (2, 3), (3, 3), (4, 3)
(iv) (1, 4), (2, 4), (3, 4), (4, 4,)
Solution:
(i) (1, 1), (1, 2), (1, 3), (1, 4)
To plot these points,
Take a point O on a graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on x-axis and y-axis 1 cm represents 1 unit.

To plot point (1, 1), we start from the origin O and move 1 cm along X - axis and 1 cm
along Y - axis. The point we arrive at is (1, 1).
To plot point (1, 2), we move 1 cm along X - axis and 2 cm along Y - axis. The point we
arrive at is (1, 2).
To plot point (1, 3), we move 1 cm along X - axis and 3 cm along Y - axis. The point we
arrive at is (1, 3).
To plot point (1, 4), we move 1 cm along X - axis and 4 cm along Y - axis. The point we
arrive at is (1, 4)

(ii) (2, 1), (2, 2), (2, 3), (2, 4)
To plot these points,
Take a point O on a graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on x-axis and y-axis 1 cm represents 1 unit.
To plot point (2, 1), we move 2 cm along X - axis and 1 cm along Y - axis. The point we
arrive at is (2, 1).
To plot point (2, 2), we move 2 cm along X - axis and 2 cm along Y - axis. The point we
arrive at is (2, 2).
To plot point (2, 3), we move 2 cm along X - axis and 3 cm along Y - axis. The point we
arrive at is (2, 3).
To plot point (2, 4), we move 2 cm along X - axis and 4 cm along Y - axis. The point we
arrive at is (2, 4).
Page 4

1. Plot the points (5, 0), (5, 1), (5, 8). Do they lie on a line? What is your observation?
Solution:
Take a point O on the graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on the x-axis and y-axis 1 cm represents 1 unit.
To plot point (5, 0), we start from the origin O and move 5 cm along X - axis. The point
we arrive at is point (5, 0).
To plot point (5, 1), we move 5 cm along X - axis and 1 cm along Y - axis. The point we
arrive at is point (5, 1).
To plot point (5, 8), we move 5 cm along X - axis and 8 cm along Y - axis. The point we
arrive at is point (5, 8).

From the above graph, we observe that all points are having same X – coordinates, it can
be seen that the points lie on a line parallel to the y-axis. Hence all points lie on the same
line.

2. Plot the points (2, 8), (7, 8) and (12, 8). Join these points in pairs. Do they lie on a
line? What do you observe?
Solution:

Take a point O on the graph paper and draw the horizontal and vertical lines OX and OY

respectively.
Then, let on the x-axis and y axis 1 cm represents 1 unit.
In order to plot point (2, 8), we start from the origin O and move 8 cm along X - axis. The
point we arrive at is (2, 8).
To plot point (7, 8), we move 7 cm along X - axis and 8 cm along Y - axis. The point we
arrive at is (7, 8).
To plot point (12, 8), we move 12 cm along X - axis and 8 cm along Y - axis. The point
we arrive at is (12, 8).

From the above graph, we observe that all points are having same Y – coordinates, it can
be seen that the points lie on a line parallel to the x-axis. Hence all points lie on the same
line.

3. Locate the points :
(i) (1, 1), (1, 2), (1, 3), (1, 4)
(ii) (2, 1), (2, 2), (2, 3), (2, 4)
(iii) (1, 3), (2, 3), (3, 3), (4, 3)
(iv) (1, 4), (2, 4), (3, 4), (4, 4,)
Solution:
(i) (1, 1), (1, 2), (1, 3), (1, 4)
To plot these points,
Take a point O on a graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on x-axis and y-axis 1 cm represents 1 unit.

To plot point (1, 1), we start from the origin O and move 1 cm along X - axis and 1 cm
along Y - axis. The point we arrive at is (1, 1).
To plot point (1, 2), we move 1 cm along X - axis and 2 cm along Y - axis. The point we
arrive at is (1, 2).
To plot point (1, 3), we move 1 cm along X - axis and 3 cm along Y - axis. The point we
arrive at is (1, 3).
To plot point (1, 4), we move 1 cm along X - axis and 4 cm along Y - axis. The point we
arrive at is (1, 4)

(ii) (2, 1), (2, 2), (2, 3), (2, 4)
To plot these points,
Take a point O on a graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on x-axis and y-axis 1 cm represents 1 unit.
To plot point (2, 1), we move 2 cm along X - axis and 1 cm along Y - axis. The point we
arrive at is (2, 1).
To plot point (2, 2), we move 2 cm along X - axis and 2 cm along Y - axis. The point we
arrive at is (2, 2).
To plot point (2, 3), we move 2 cm along X - axis and 3 cm along Y - axis. The point we
arrive at is (2, 3).
To plot point (2, 4), we move 2 cm along X - axis and 4 cm along Y - axis. The point we
arrive at is (2, 4).

(iii) (1, 3), (2, 3), (3, 3), (4, 3)
To plot these points,
Take a point O on a graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on x-axis and y-axis 1 cm represents 1 unit.
To plot point (1, 3), we move 1 cm along X - axis and 3 cm along Y - axis. The point we
arrive at is (1, 3).
To plot point (2, 3), we move 2 cm along X - axis and 3 cm along Y - axis. The point we
arrive at is (2, 3).
To plot point (3, 3), we move 3 cm along X - axis and 3 cm along Y - axis. The point we
arrive at is (3, 3).
To plot point (4, 3), we move 4 0cm along X - axis and 3 cm along Y - axis. The point we
arrive at is (4, 3).

Page 5

1. Plot the points (5, 0), (5, 1), (5, 8). Do they lie on a line? What is your observation?
Solution:
Take a point O on the graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on the x-axis and y-axis 1 cm represents 1 unit.
To plot point (5, 0), we start from the origin O and move 5 cm along X - axis. The point
we arrive at is point (5, 0).
To plot point (5, 1), we move 5 cm along X - axis and 1 cm along Y - axis. The point we
arrive at is point (5, 1).
To plot point (5, 8), we move 5 cm along X - axis and 8 cm along Y - axis. The point we
arrive at is point (5, 8).

From the above graph, we observe that all points are having same X – coordinates, it can
be seen that the points lie on a line parallel to the y-axis. Hence all points lie on the same
line.

2. Plot the points (2, 8), (7, 8) and (12, 8). Join these points in pairs. Do they lie on a
line? What do you observe?
Solution:

Take a point O on the graph paper and draw the horizontal and vertical lines OX and OY

respectively.
Then, let on the x-axis and y axis 1 cm represents 1 unit.
In order to plot point (2, 8), we start from the origin O and move 8 cm along X - axis. The
point we arrive at is (2, 8).
To plot point (7, 8), we move 7 cm along X - axis and 8 cm along Y - axis. The point we
arrive at is (7, 8).
To plot point (12, 8), we move 12 cm along X - axis and 8 cm along Y - axis. The point
we arrive at is (12, 8).

From the above graph, we observe that all points are having same Y – coordinates, it can
be seen that the points lie on a line parallel to the x-axis. Hence all points lie on the same
line.

3. Locate the points :
(i) (1, 1), (1, 2), (1, 3), (1, 4)
(ii) (2, 1), (2, 2), (2, 3), (2, 4)
(iii) (1, 3), (2, 3), (3, 3), (4, 3)
(iv) (1, 4), (2, 4), (3, 4), (4, 4,)
Solution:
(i) (1, 1), (1, 2), (1, 3), (1, 4)
To plot these points,
Take a point O on a graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on x-axis and y-axis 1 cm represents 1 unit.

To plot point (1, 1), we start from the origin O and move 1 cm along X - axis and 1 cm
along Y - axis. The point we arrive at is (1, 1).
To plot point (1, 2), we move 1 cm along X - axis and 2 cm along Y - axis. The point we
arrive at is (1, 2).
To plot point (1, 3), we move 1 cm along X - axis and 3 cm along Y - axis. The point we
arrive at is (1, 3).
To plot point (1, 4), we move 1 cm along X - axis and 4 cm along Y - axis. The point we
arrive at is (1, 4)

(ii) (2, 1), (2, 2), (2, 3), (2, 4)
To plot these points,
Take a point O on a graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on x-axis and y-axis 1 cm represents 1 unit.
To plot point (2, 1), we move 2 cm along X - axis and 1 cm along Y - axis. The point we
arrive at is (2, 1).
To plot point (2, 2), we move 2 cm along X - axis and 2 cm along Y - axis. The point we
arrive at is (2, 2).
To plot point (2, 3), we move 2 cm along X - axis and 3 cm along Y - axis. The point we
arrive at is (2, 3).
To plot point (2, 4), we move 2 cm along X - axis and 4 cm along Y - axis. The point we
arrive at is (2, 4).

(iii) (1, 3), (2, 3), (3, 3), (4, 3)
To plot these points,
Take a point O on a graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on x-axis and y-axis 1 cm represents 1 unit.
To plot point (1, 3), we move 1 cm along X - axis and 3 cm along Y - axis. The point we
arrive at is (1, 3).
To plot point (2, 3), we move 2 cm along X - axis and 3 cm along Y - axis. The point we
arrive at is (2, 3).
To plot point (3, 3), we move 3 cm along X - axis and 3 cm along Y - axis. The point we
arrive at is (3, 3).
To plot point (4, 3), we move 4 0cm along X - axis and 3 cm along Y - axis. The point we
arrive at is (4, 3).

(iv) (1, 4), (2, 4), (3, 4), (4, 4,)
To plot these points,
Take a point O on a graph paper and draw horizontal and vertical lines OX and OY
respectively.
Then, let on x-axis and y-axis 1 cm represents 1 unit.
In order to plot point (1, 4), we move 1 cm along X - axis and 4 cm along Y - axis. The
point we arrive at is (1, 4).
To plot point (2, 4), we move 2 cm along X - axis and 4 cm along Y - axis. The point we
arrive at is (2, 4).
To plot point (3, 4), we move 3 cm along X - axis and 4 cm along Y- axis. The point we
arrive at is (3, 4).
To plot point (4, 4), we move 4 cm along X - axis and 4 cm along Y - axis. The point we
arrive at is (4, 4).

4. Find the coordinates of points A, B, C, D in Fig. 27.7
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