**Introduction to Graphs**

**Question 1.****Plot the following points on a graph sheet. Verify if they lie on a line(a)** A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)

**(b)**P(1, 1), Q(2, 2), R(3, 3), S(4, 4)

**(c)**K(2, 3), L(5, 3), M(5, 5), N(2, 5).

**Solution:****(a)** Draw the x-axis and y-axis. Plot the points A(4, 0), B(4, 2), C(4, 6) and D(4, 2.5) as shown. Clearly, these points lie on a line ABDC.

Clearly, these points lie on a line PQRS.**(c)** Draw the x-axis and y-axis. Plot the points K(2, 3), L(5, 3), M(5, 5) and N(2, 5) as shown.

Clearly, these points do not lie on a 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:**

Draw the x-axis and y-axis. Plot the points P(2, 3) and Q(3, 2). Join PQ and produce PQ on both sides to meet the x-axis at A and y-axis atB. Clearly, the coordinates of A and B are (5, 0) and (0, 5) respectively.

**Question 3.****Write the coordinates of the vertices of each of these adjoining figures.**

**Solution:**

Clearly, from the graph the coordinates of points are :

O(0, 0), A(2, 0), B(2, 3) and C(0, 3);

P(4, 3), Q(6, 1), R(6, 5) and S(4, 7);

L(7, 7), M(10, 8) and k(10, 5).

**Question 4.****State whether True or False. Correct that 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-coordinate is zero and x-coordinate is 5 will lie on y-axis.

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

**Solution:****(i)** True.**(ii)** False. Correct statement is : A point whose y-coordinate is zero and x-coordinate is 5 will he on x-axis.**(iii)** True.