In this chapter, we provide RD Sharma Solutions for Class 8 Chapter 27 Introduction to Graphs Exercise 27.1 for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Class 8 Chapter 27 Introduction to Graphs Exercise 27.1 pdf, free RD Sharma Solutions for Class 8 Chapter 27 Introduction to Graphs Exercise 27.1 book pdf download. Now you will get step by step solution to each question.
Access RD Sharma Solutions For Class 8 Maths Exercise 27.1 Chapter 27 Introduction to Graphs
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
Solution:
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 above 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 C are (4, 6).
DZ = 5 units and DR= 3 units
So, the coordinates of vertex D are (5, 3).
5. Find the coordinates of points P, Q, R and S in Fig. 27.8.
Solution:
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
So, the coordinates of vertex P are (10, 70).
QF = 12 units and QB = 80 units
So, the coordinates of vertex Q are (12, 80).
RG = 16 units and RC = 100 units
So, the coordinates of vertex R are (16, 100).
SH = 20 units and SD = 120 units
So, the coordinates of vertex S are (20, 120).
6. Write the coordinates of each of the vertices of each polygon in Fig. 27.9.
Solution:
From the figure, we have:
In Quadrilateral 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
So, the coordinates of D are (3, 3).
AE = 4 units and AH = 5 units
So, the coordinates of A are (4, 5).
CF = 6 units and CI = 3 units
So, the coordinates of C are (6, 3).
BE = 7 units and BJ = 5 units
So, 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
So, the coordinates of P are (7, 4).
QE = 9 units and QK = 5 units
So, the coordinates of Q are (9, 5).
RF = 9 units and RK = 3 units
So, the coordinates of R are (9, 3)
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.
Solution:
(i) A point whose x-coordinate is zero, will lie on the y-axis.
From the figure,
For x = 0, we have x- coordinates as zero.
For example (0, 3), (0, 6), (0, 9)
These points will lie on y axis. Hence, we say that our given statement is true.
(ii) A point whose y-coordinate is zero, will lie on x-axis.
A point whose y-coordinate is zero, will lie on x-axis.
For y = 0, we have y- coordinates as zero.
For example (3, 0), (6, 0), (9, 0)
These points will lie on x axis. Hence, we say that our given statement is true.
(iii) The coordinates of the origin are (0, 0).
Origin is intersection of x-axis and y-axis. This means that coordinates of the origin will be intersection of lines y = 0 and x = 0.
Hence, coordinates of origin are (0, 0).
∴ Given statement is true.
(iv) Points whose x and y coordinates (0, 0), (1, 1), (2, 2) etc are equal, lie on a line passing through the origin.
For above statement we can conclude that our statement satisfies the equation x = y.
For x = 0 and y = 0, this equation gets satisfied.
∴ Given statement is true.
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