Show the number 3 on the number line.

Consider a point P on the number line such that O P = 1 unit and draw a line m perpendicular to the number line such that P S = 1 unit. Applying Pythagoras theorem, we get, O S 2 = O P 2 + P S 2 O S = 2 unit. Draw an arc with centre O and radius O S . Mark the point of intersection of the number line and the point as Q such that O Q = 2 unit. Represent a point Q such that Q = 2 on the number line. Draw a line l perpendicular to the number line through the point Q Take a point R on the line l such that it is at unit distance from Q on the line. Draw a segment O R such that a right angled triangle ∆ O R Q is formed. Now, using Pythagoras theorem, O R 2 = O Q 2 + Q R 2 O R 2 = 2 2 + 1 2 O R 2 = 3 or O R = 3 Draw an arc with centre O and radius O R . Mark the point of intersection of the line and the arc as C . The point C shows the number 3

Show the number 5 on the number line.

Represent a point A such that O A = 2 units on the number line. Draw a line X perpendicular to the number line through the point A Take a point B on the line A X such that it is at unit distance from A . Draw a segment O B such that a right angled triangle ∆ O A B is formed. Now, using Pythagoras theorem, O B 2 = O A 2 + A B 2 O B 2 = 2 2 + 1 2 O B 2 = 5 or O B = 5 Draw an arc with centre O and radius O B . Mark the point of intersection of the line and the arc as C . The point C shows the number 5

Show the number 7 on the number line.

Steps of construction: Draw a number line. Let O be the origin on the number line l . Let A be on the line such that OA = 1 unit. Draw AB perpendicular to OA at A such that AB = 1 unit. Then OB 2 = OA 2 + AB 2 = 1 2 + 1 2 = 2 . Thus OB = 2 units. With O as centre and OB as radius drawn an arc cutting the line at C . Then OC = OB = 2 units Again draw CD perpendicular to l such that CD = 1 unit. Then OD 2 = OC 2 + CD 2 = 2 + 1 = 3 . Thus OD = 3 units. Draw an arc with O as centre and OD as radius to cut l in E . Then OE = OD = 3 units. Draw EF perpendicular to l at E such that EF = 2 units and join OF . Now OF 2 = OE 2 + EF 2 = 3 + 4 = 7 . Hence, OF = 7 units. With O as centre and OF as radius, cut l at G . Then OG = OF = 7 units. Thus OG represents 7 on number line.