Represent 5 on number line.

To find: 5 on number line. Draw a number line as shown in the figure. Let the point A represent 0 (zero) and point B represents 2 . Draw perpendicular BX at B on the number line and cut-off arc BC = 1 unit . We have AB = 2 units and BC = 1 unit According to Pythagoras theorem in ∆ ABC , Hypotenuse 2 = Base 2 + Side 2 ⇒ AC 2 = 2 2 + 1 2 ⇒ AC 2 = 4 + 1 ⇒ AC 2 = 5 ⇒ AC = 5 Now, using a compass taking A as the center and AC = 5 as radius draw an arc intersecting the real line at P . Clearly, AP = AC = 5 . Hence, P represents 5 on the number line as shown in the figure below.

Construct a line segment corresponding to 13

To construct a line segment of measure 13 Draw a number line as shown in the figure. Let the point A represent 0 (zero) and point B represents 3 . Draw perpendicular BX at B on the number line and cut-off arc BC = 2 units . Now, we have AB = 3 units and BC = 2 units According to Pythagoras theorem in ∆ ABC , Hypotenuse 2 = Base 2 + Side 2 ⇒ AC 2 = 3 2 + 2 2 ⇒ AC 2 = 9 + 4 ⇒ AC 2 = 13 ⇒ AC = 13 Now, using a compass taking A as the centre and AC = 13 unit as radius draw an arc intersecting the real line at P . Clearly, AP = AC = 13 . Hence, P represents 13 on the number line and AP is the line segment corresponding to 13 as shown in the figure below.