# NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs (EX 15.2) Exercise 15.2

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Exercise 15.2

Refer to page 9 for Exercise 15.2 in the PDF

1. Plot the following points on a graph sheet. Verify if they lie on a line

(a) $A\left( {4,{\text{ }}0} \right),{\text{ }}B\left( {4,{\text{ }}2} \right),{\text{ }}C\left( {4,{\text{ }}6} \right),{\text{ }}D\left( {4,{\text{ }}2.5} \right)$

Ans: To plot $A\left( {4,{\text{ }}0} \right)$ start at $O(0,0)$ and then move 4 units to its right, then move 3 units up, you reach the point $A\left( {4,{\text{ }}0} \right)$.

To plot $B\left( {4,{\text{ }}2} \right)$ start at $O(0,0)$ and then move 4 units to its right, then move 2 units up, you reach the point $B\left( {4,{\text{ }}2} \right)$.

To plot ${\text{ }}C\left( {4,{\text{ }}6} \right)$ start at $O(0,0)$ and then move 4 units to its right, then move 6 units up, you reach the point ${\text{ }}C\left( {4,{\text{ }}6} \right)$.

To plot $D\left( {4,{\text{ }}2.5} \right)$ start at $O(0,0)$ and then move 4 units to its right, then move 2.5 units up, you reach the point $D\left( {4,{\text{ }}2.5} \right)$.

Now join all these four points. The graph will look like:

(Image Will Be Updated Soon)

In the graph , it is obvious that all four points lie on a line.

(b) $P\left( {1,{\text{ }}1} \right),{\text{ }}Q\left( {2,{\text{ }}2} \right),{\text{ }}R\left( {3,{\text{ }}3} \right),{\text{ }}S\left( {4,{\text{ }}4} \right)$

Ans: To plot $P\left( {1,{\text{ }}1} \right)$ start at $O(0,0)$ and then move 1 unit to its right, then move 1 unit up, you reach the point $P\left( {1,{\text{ }}1} \right)$.

To plot $Q\left( {2,{\text{ }}2} \right)$ start at $O(0,0)$ and then move 2 units to its right, then move 2 units up, you reach the point $Q\left( {2,{\text{ }}2} \right)$.

To plot $R\left( {3,{\text{ }}3} \right)$ start at $O(0,0)$ and then move 3 units to its right, then move 3 units up, you reach the point $R\left( {3,{\text{ }}3} \right)$.

To plot $S\left( {4,{\text{ }}4} \right)$ start at $O(0,0)$ and then move 4 units to its right, then move 4 units up, you reach the point $S\left( {4,{\text{ }}4} \right)$.

Now join all these four points. The graph will look like:

(Image Will Be Updated Soon)

In the graph , it is obvious that all four points lie on a line.

(c) $K\left( {2,{\text{ }}3} \right),{\text{ }}L\left( {5,{\text{ }}3} \right),{\text{ }}M\left( {5,{\text{ }}5} \right),{\text{ }}N\left( {2,{\text{ }}5} \right)$

Ans: To plot $K\left( {2,{\text{ }}3} \right)$ start at $O(0,0)$ and then move 2 unit to its right, then move 3 unit up, you reach the point $K\left( {2,{\text{ }}3} \right)$.

To plot $L\left( {5,{\text{ }}3} \right)$ start at $O(0,0)$ and then move 5 units to its right, then move 3 units up, you reach the point $L\left( {5,{\text{ }}3} \right)$

To plot $M\left( {5,{\text{ }}5} \right)$ start at $O(0,0)$ and then move 5 units to its right, then move 5 units up, you reach the point$M\left( {5,{\text{ }}5} \right)$.

To plot $N\left( {2,{\text{ }}5} \right)$ start at $O(0,0)$ and then move 2 units to its right, then move 5 units up, you reach the point$N\left( {2,{\text{ }}5} \right)$.

Now join all these four points. The graph will look like:

(Image Will Be Updated Soon)

Joining all four points gives a rectangle. Thus, all four points do not lie on a line.

2. Draw the line passing through (2, 3) and (3, 2). Find the coordinates of the points at which this line meets the x-axis and y-axis.

Ans: To plot $\left( {2,{\text{ }}3} \right)$start at $O(0,0)$and then move 2 units to its right, then move 3 units up, you reach the point$\left( {2,{\text{ }}3} \right)$.

To plot $(3,2)$ start at $O(0,0)$and then move 3 units to its right, then move 2 units up, you reach the point $(3,2)$.

Now join both the points, you will get a line segment. Now extend  this line segment on both sides to get the line.

The graph will look like:

(Image Will Be Updated Soon)

In the given graph, one can observe that Coordinates of the points where the  line meets x-axis is $(5,0)$ and y-axis is $(0,5)$.

3. Write the coordinates of the vertices of each of these adjoining figures:

(Image Will Be Updated Soon)

Let’s  consider the vertex O:

O is 0 units right to the origin and 0 units up from the origin. Thus, $O(0,0)$.

Let’s first consider the vertex A:

A is 2 units right to the origin and 0 units up from the origin. Thus, $A(2,0)$.

Let’s first consider the vertex B:

B is 2 units right to the origin and 3 units up from the origin. Thus, $B(2,3)$.

Let’s first consider the vertex C:

C is 0 units right to the origin and 3 units up from the origin. Thus, $C(0,3)$.

Let’s first consider the vertex P:

P is 4 units right to the origin and 3 units up from the origin. Thus, $P(4,3)$.

Let’s first consider the vertex Q:

Q is 6 units right to the origin and 1 unit up from the origin. Thus, $Q(6,1)$.

Let’s first consider the vertex R:

R is 6 units right to the origin and 5 units up from the origin. Thus, $R(6,5)$.

Let’s first consider the vertex S:

S is 4 units right to the origin and 7 units up from the origin. Thus, $S(4,7)$.

Let’s first consider the vertex K:

K is 10 units right to the origin and 5 units up from the origin. Thus, $K(10,5)$.

Let’s first consider the vertex L:

L is 7 units right to the origin and 7 units up from the origin. Thus, $L(7,7)$.

Let’s first consider the vertex M:

M is 10 units right to the origin and 8 units up from the origin. Thus, $M(10,8)$.

Thus,

$O{\text{ }}\left( {0,{\text{ }}0} \right),{\text{ }}A{\text{ }}\left( {2,{\text{ }}0} \right),{\text{ }}B{\text{ }}\left( {2,{\text{ }}3} \right),{\text{ }}C{\text{ }}\left( {0,{\text{ }}3} \right){\text{ }}P{\text{ }}\left( {4,{\text{ }}3} \right),{\text{ }}Q{\text{ }}\left( {6,{\text{ }}1} \right),{\text{ }}R{\text{ }}\left( {6,{\text{ }}5} \right),{\text{ }}S{\text{ }}\left( {4,{\text{ }}7} \right){\text{ }}K{\text{ }}\left( {10,{\text{ }}5} \right),{\text{ }}L{\text{ }}\left( {7,{\text{ }}7} \right),{\text{ }}M{\text{ }}\left( {10,{\text{ }}8} \right)$

4. State whether True or False. Correct those are false.

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

Ans: x coordinate is zero implies that the point lies 0 units right to the $O(0,0)$ and y-axis is 0 units right to the $O(0,0)$, i.e., a point with x coordinate 0 will always lie on the y-axis. Therefore, A point whose x coordinate is 0 and y coordinate is non-zero will lie on the y-axis.

Thus, the given statement is true.

(ii) A point whose y coordinate is zero and x-coordinate is 5 will lie on the y-axis.

Ans: y coordinate is zero implies that the point lies 0 units up from the $O(0,0)$ and x-axis is 0 units up from the $O(0,0)$, i.e., a point with y coordinate 0 will always lie on x-axis. Therefore, A point whose y coordinate is 0 and x coordinate is 5 will lie on the x-axis.

Thus, the given statement is false.

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

Ans: The given statement is true.

## NCERT Solutions For Class 8 Maths Chapter 15 Introduction To Graphs (Ex 15.2) Exercise 15.2

Opting for the NCERT solutions for Ex 15.2 Class 8 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 15.2 Class 8 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

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