RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Mathematics

Created by: Abhishek Kapoor

Class 8 : RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev

The document RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
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PAGE NO 27.5:

Question 1:

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

Ans:

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.
In order to plot point (5, 0), we start from the origin O and move 5 cm along OX. The point we arrive at is point (5,0).
To plot point (5, 1), we move 5 cm along OX and 1 cm along OY. The point we arrive at is point (5,1).
To plot point (5,8), we move 5 cm along OX and 8 cm along OY. The point we arrive at is point (5,8).
From the graph below, it can be seen that the points lie on a line parallel to y-axis. This is because they have the same x-coordinate.
RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev


Question 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?

Ans:

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 OX. The point we arrive at is (2, 8).
To plot point (7, 8), we move 7 cm along OX and 8 cm along OY. The point we arrive at is (7, 8).
To plot point (12, 8), we move 12 cm along OX and 8 cm along OY. The point we arrive at is (12,8).
From the graph below, it can be seen that the points lie on a line parallel to x-axis because they have the same y-coordinate.
RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev


Question 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).

Ans:

(i) In order to plot these points, the given steps are to be followed:
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, 1), we start from the origin O and move 2 cm along OX and 1 cm along OY. The point we arrive at is (1, 1).
To plot point (1, 2), we move 1 cm along OX and 2 cm along OY. The point we arrive at is (1, 2).
To plot point (1, 3), we move 1 cm along OX and 3 cm along OY. The point we arrive at is (1, 3).
To plot point (1, 4), we move 1 cm along OX and 4 cm along OY. The point we arrive at is (1, 4).
RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev

(ii) Follow the steps mentioned in point (i).
RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev

(iii) Follow the steps mentioned in point (i).
RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev

(iv) Follow the steps mentioned in point (i).

RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev


PAGE NO 27.6:

Question 4:

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

RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev

Ans:

RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev
Draw perpendiculars AP, BP, CQ and DR from A, B, C and D on the x-axis. Also, draw perpendiculars AW, BX, CY and DZ on the y-axis.
From the figure, we have:
AW = 1 unit and AP= 1 unit
So, the coordinates of vertex A are (1, 1).
Similarly, BX=1 unit and BP= 4 units
So, the coordinates of vertex B are (1, 4).
CY = 4 units and CQ= 6 units
So, the coordinates of vertex B are (4, 6).
DZ = 5 units and DR= 3 units
So, the coordinates of vertex B are (5, 3).


Question 5:

Find the coordinates of points P, Q, R and S in Fig. 27.8.
RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev

Ans:

RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev
Draw perpendiculars PA, QB, RC and SD from vertices P, Q, R and S on the x-axis. Also ,draw perpendiculars
PE, QF, RG and SH on the y-axis from these points.

PE = 10 units and  PA = 70 units
Therefore, the coordinates of vertex P are (10, 70).
QF = 12 units and  QB = 80 units
Therefore, the coordinates of vertex Q are (12, 80).
RG = 16 units and  RC = 100 units
Therefore, the coordinates of vertex R are (16, 100).
SH = 20 units and  SD = 120 units
Therefore, the coordinates of vertex S are (20, 120).


Question 6:

Write the coordinates of each of the vertices of each polygon in Fig. 27.9.
RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev

Ans:

RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev

From the figure, we have:
In polygon OXYZ:
O lies on the origin and the coordinates of the origin are (0, 0). So, the coordinates of O are (0, 0).
X lies on the y-axis. So, the x-coordinate is 0. Hence, the coordinate of X is (0, 2).
Also, YX is equal to 2 units and YZ is equal to 2 units. So, the coordinates of vertex Y are (2, 2).
Z lies on the x-axis. So, the y-coordinate is 0. Hence, the coordinates of Z are (2, 0).

In polygon ABCD:
Draw perpendiculars DG, AH, CI and BJ from A, B, C and D on the x-axis.
Also, draw perpendiculars DF, AE, CF and BE from A, B, C and D on the y-axis.
Now, from the figure:
DF = 3 units and DG = 3 units
Therefore, the coordinates of D are (3, 3).
AE = 4 units and AH = 5 units
Therefore, the coordinates of A are (4, 5).
CF = 6 units and CI = 3 units
Therefore, the coordinates of C are (6, 3).
BE = 7 units and BJ = 5 units
Therefore, the coordinates of B are (7, 5).

In polygon PQR:
Draw perpendiculars PJ, QK and RK from P, Q and R on the x-axis.
Also, draw perpendiculars PW, QE and RF from P, Q and R on the y-axis.
Now, from the figure:
PW = 7 units and PJ = 4 units
Therefore, the coordinates of P are (7, 4).
QE = 9 units and QK = 5 units
Therefore, the coordinates of Q are (9, 5).
RF = 9 units and RK = 3 units
Therefore, the coordinates of R are (9, 3).


PAGE NO 27.7:

Question 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.

Ans:

(i) The examples of points having x-coordinate as zero are (0,3), (0,6), (0,9). This can be represented in the following manner:
RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev
From the figure, it can be seen that these points lie on the y-axis. Hence, the statement is true.
(ii) The examples of points having y-coordinate as zero are (3,0), (6,0), (9,0). This can be represented in the following manner:

RD Sharma Solutions - Chapter 27 - Introduction to Graphs (Part - 2), Class 8, Maths Class 8 Notes | EduRev

From figure above, it can be seen that these points lie on the x-axis. Hence, the statement is true.
(iii) The origin divides each of these axes into a positive and a negative semi-axis. The coordinates of the origin are always are zero, i.e. (0,0). Thus, the statement is true.
(iv) The examples of points having equal x and y coordinates are (0,0), (1,1), (2,2), etc. If these points are joined, they will lie on a line passing through the coordinates (0,0). Thus, the statement is true.

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