Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Introduction to Graphs - Exercise 27.1
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Page 1
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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FAQs on Introduction to Graphs - Exercise 27.1 - Mathematics (Maths) Class 8
| 1. What is a graph in the context of computer science? |  |
Ans. In computer science, a graph is a data structure that consists of a set of nodes (also known as vertices) and a set of edges that connect these nodes. It is used to represent relationships between different entities or elements.
| 2. How are graphs useful in computer science? | |
Ans. Graphs are widely used in computer science for various purposes. They can be used to represent networks, such as social networks or computer networks. Graphs are also used in algorithms for tasks like finding the shortest path between two nodes, detecting cycles, or solving optimization problems.
| 3. What are the different types of graphs? | |
Ans. There are several types of graphs in computer science. Some common types include directed graphs, where edges have a specific direction, undirected graphs, where edges have no specific direction, weighted graphs, where edges have associated weights or costs, and bipartite graphs, where nodes can be divided into two distinct sets.
| 4. How can graphs be implemented in computer programs? | |
Ans. Graphs can be implemented in computer programs using various data structures. One common approach is to use an adjacency matrix, where a matrix is used to represent the connections between nodes. Another approach is to use an adjacency list, where each node is associated with a list of its neighboring nodes.
| 5. What are some real-world applications of graphs? | |
Ans. Graphs have numerous real-world applications. They are used in social network analysis, route planning and navigation systems, recommendation systems, data mining, and many other areas. For example, graph algorithms can be used to find the shortest path between two locations in a map or to determine the influence of individuals in a social network.
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Dec 18, 2024 Last updated |
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These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
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Introduction to Graphs - Exercise 27.1 Notes
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