# Exercise 15.2 Introduction to Graphs- NCERT Solutions Class 8

Introduction to Graphs

Exercise 15.2

## Question 1

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

(a)

\(\rm{A(4,0),{{B}}(4,2),{{C}}(4,6),{{D}}(4,2.5)}\)

(b)

\(\rm{P(1,1),\;{{Q}}(2,2),\;{{R}}(3,3),\;{{S}}(4,4)}\)

(c)

\(\rm{K(2,3),\; L( (5,3),\;M(5,5),\;N(2,5)}\)

### Solution

**Video Solution**

**Reasoning:**

Consider \(x\)-axis and \(y\)-axis as a number line starting from (\(0,0\)). And locate the given points.

**Steps:**

(a) We can plot the given points and join the consecutive points on a graph paper as follows.

From the graph, it can be observed that the points \(A, B, C,\) and \(D\) lie on the same line.

(b) We can plot the given points and join the consecutive points on a graph paper as follows.

Hence, points \(P, Q, R,\) and \(S\) lie on the same line.

(c) We can plot the given points and join the consecutive points on a graph paper as follows.

Hence, points\( K, L, M, \)and \(N\) are not lying on the same line.

## Question 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.

### Solution

**Video Solution**

**Steps:**

From the graph, it can be observed that the line joining the points (\(2, 3\)) and (\(3, 2\)) meets the x-axis at the point (\(5, 0\)) and the y-axis at the point (\(0, 5\)).

## Question 3

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

### Solution

**Video Solution**

**Reasoning:**

\(x\)-axis and \(y\)-axis are represented as a number line starting from (\(0,0\)). Locate the numerical value of the given points.

**Steps:**

The coordinates of the vertices in the given figure are as follows.

\[\begin{align}&{{O(0,0), A(2,0), B(2,3),C(0,3)}}\\&{{P(4,3), Q(6,1), R(6,5),S(4,7)}}\\&{{K(10,5), L(7,7),M (10,8)}}\end{align}\]

## Question 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.

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

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

### Solution

**Video Solution**

**Steps:**

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

(ii) A point whose \(y-\)co-ordinate is zero and \(x-\)coordinate is \(5\) will lie on \(y-\)axis.: **False**

The point whose \(y-\)coordinate is zero and \(x-\)coordinate is \(5\) will lie on \(x-\)axis.

(iii) The coordinates of the origin are (\(0, 0\)).: **True**

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