Show how can be represented on the number line.

Steps of construction:

Step 1: Let AB be a line of length 2 unit on the number line


Step 2: At B, draw a perpendicular line BC of length 1 unit and then join CA


Step 3: Now, ABC is a right angled triangle.


Using Pythagoras theorem,


AB2 + BC2 = CA2


22 + 12 = CA2


CA2 = 5


CA =


Thus, CA is a line of length unit


Step 4: Taking CA as a radius and A as the center, construct an arc touching the number line.


The number line gets intersected by arc at point which is distance from 0 as it is a radius of the circle with center A


Thus, is represented on the number line as shown in the figure below



26