State whether the statement: Every point on the number line is of the form m , where m is a natural number is true or false. Justify your answer.

On number line positive numbers are placed to the right of zero and negative numbers are placed to the left of zero. We know that, Square root of negative numbers cannot be determined. Therefore, The negative numbers on the number line cannot be expressed in the form m . Hence, The given statement is false.

Show how 5 can be represented on the number line.

To represent 5 on the number line, take O A = 2 units and make a perpendicular at A , so that A B = 1 unit , as shown in the figure. Then, ∆ O A B is a right-angled triangle So, by applying Pythagoras theorem, we get, O B 2 = O A 2 + A B 2 . ⇒ O B 2 = 2 2 + 1 2 ⇒ O B 2 = 5 ⇒ O B = 5 units . Now, taking O as Centre and O B as radius, draw an arc intersecting the number line at P . Hence, O P is the required distance that represents 5 .