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