Solution of Chapter 27. Introduction to Graphs (RD Sharma - Mathematics Book)

Exercise 27.1

1

Plot the points (5,0), (5,1), (5,8). Do thy lie on a line? What is your observation?

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?

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,)

4

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

5

Find the coordinates of points P, Q, R and S in Fig. 27.8.

6

Write the coordinates of each of the vertices of each polygon in Fig. 27.9.

7

Decide which of the following statements is true and which is false. Give reasons for your answer.

(i) A point whose x-coordinate is zero, will lie on the y-axis.

(ii) A point whose y-coordinate is zero, will lie on x-axis.

(iii) The coordinates of the origin are (0,0).

(iv) Points whose x and y coordinates are equal, lie on a line passing through the origin.

Exercise 27.2

1

The following table shows the number of patients discharged from a hospital with HIV diagnosis in different years:

 Years: 2002 2003 2004 2005 2006 Number of patients: 150 170 195 225 230

Represent this information by a graph.

2

The following table shows the amount of rice grown by a farmer in different years:

 Years: 2000 2001 2002 2003 2004 2005 2006 Rice grown(in quintals): 200 180 240 260 250 200 270

Plot a graph to illustrate this information.

3

The following table gives the information regarding the number of persons employed to a piece of work and time taken to complete the work:

 Number of persons: 2 4 6 8 Time taken (in days): 12 6 4 3

Plot a graph of this information.

4

The following table gives the information regarding length of a side of a square and its area

 Length of a side (in cm) 1 2 3 4 5 Area of square (in cm2) 1 4 9 16 25

Draw a graph to illustrate this information.

5

The following table shows the sales of a commodity during the years 2000 to 2006.

 Years 2000 2001 2002 2003 2004 2005 2006 Sales(in lakhs of Rs.) 1.5 1.8 2.4 3.2 5.4 7.8 8.6

Draw a graph of this information.

6

Draw the temperature-time graph in each of the following cases:

(i)

 Time (in hours) 7:00 9:00 11:00 13:00 15:00 17 19:00 21:00 Temperature (°F) in 100 101 104 102 100 99 100 98

(ii)

 Time (in hours) 8:00 10:00 12:00 14:00 16:00 18:00 20:00 Temperature (°F) in 100 101 104 103 99 98 100
7

Draw the velocity-time graph from the following data :

 Time (in hours) 7:00 8:00 9:00 10:00 11:00 12 13:00 14:00 Speed (in km/hr) 30 45 60 50 70 50 40 45

8

The runs scored by a cricket team in first 15 overs are given below :

 Overs : I II III IV V VI VII VIII IX X XI XII XIII XIV XV Runs : 2 1 4 2 6 8 10 21 5 8 3 2 6 8 12