Represent 5 on the number line.

Draw a number line. Take a point O which is corresponding to zero. Consider a point A so that O A = 2 units. Construct a perpendicular at A and name it as A Z . Draw a cut off arc A B = 1 unit On the basis of Pythagoras Theorem, we know that: O B 2 = O A 2 + A B 2 ⇒ O B 2 = 2 2 + 1 2 ⇒ O B 2 = 4 + 1 ⇒ O B 2 = 5 . ⇒ O B = 5 . Considering O as the centre and O B = 5 as the radius construct an arc which cuts the line at the point C . Thus, O B = O C = 5 5 is represented by point C on the number line. Hence, required diagram given above.

Locate 3 on the number line.

Given, 3 Take a point O corresponding to zero. Consider a point A so that OA = 1 unit. Construct a perpendicular at A and name it as AZ . Draw an arc such that AB = 1 unit. Applying Pythagoras Theorem on △ AOB , Therefore, OB 2 = OA 2 + AB 2 ⇒ OB 2 = 1 2 + 1 2 ⇒ OB 2 = 1 + 1 ⇒ OB = 2 Therefore, OB = 2 Considering O as the centre and OB = 2 as the radius, construct an arc which cuts the number line at the point C . Thus, OB = OC = 2 Draw a perpendicular at C and name it as CY . Draw an arc of radius 1 unit which cut CY at E . Applying Pythagoras Theorem on △ OCE , we get, OE 2 = OC 2 + CE 2 ⇒ OE 2 = ( 2 ) 2 + 1 2 ⇒ OE 2 = 2 + 1 ⇒ OE 2 = 3 Therefore, OE = 3 Considering O as the centre and OE = 3 as the radius, construct an arc which cuts the number line at the point D . Thus, OD = OE = 3 Hence, 3 is represented by point D on the number line.

Locate 10 on the number line.

Given, 10 Take a point O representing 0 on the number line. Consider a point A on the number line such that OA = 3 units. Construct a perpendicular at A and name it as AZ With centre A and radius 1 unit, draw an arc cutting AZ at B such that AB = 1 unit. Applying Pythagoras theorem in △ OAB , we get, OB 2 = OA 2 + AB 2 ⇒ OB 2 = 3 2 + 1 2 ⇒ OB 2 = 9 + 1 ⇒ OB 2 = 10 Therefore, OB = 10 Considering O as the centre and OB = 10 as the radius, construct an arc which cuts the number line at the point C . Thus, OB = OC = 10 Therefore, 10 is represented by point C on the number line.

Locate 8 on the number line.

Given, 8 Take a point O which represents 0 on the number line. Consider a point A on the number line such that O A = 2 units. Construct a perpendicular at A and name it as A Z . With centre A and radius 2 unit draw an arc cutting A Z at B such that A B = 2 units. Applying Pythagoras Theorem in △ OAB , we get, O B 2 = O A 2 + A B 2 ⇒ O B 2 = 2 2 + 2 2 ⇒ O B 2 = 4 + 4 ⇒ O B 2 = 8 ⇒ O B = 8 Considering O as the centre and O B = 8 as the radius, construct an arc which cuts the number line at the point C . Therefore, 8 is represented by point C on the number line.

Represent 4 . 7 geometrically on the number line.

Construct a line segment of A B = 4 . 7 units. Extend it from B to C where BC = 1 unit. Let, O be the midpoint of A C . Let, O be the centre and O A be the radius, construct a semicircle. Draw, a perpendicular at B and name it as B D intersecting the semicircle at D . Thus, B D = 4 . 7 units Considering B as the centre and B D as the radius, construct an arc meeting the point E on A C . Thus, B E = B D = 4 . 7 units Hence, 4 . 7 is represented by point E on the number line.

Represent 10 . 5 on the number line.

Given to represent 10 . 5 on the number line. Steps of construction: 1 . Draw a line segment, O B = 10 . 5 units 2 . Extend it from B to C where B C = 1 unit. 3 . Find the midpoint of O C , say D . 4 . With D as the centre and construct a semicircle passing through O and C . 5 . Draw a perpendicular at B and name it as B E intersecting the semicircle at E . 6 . Considering B as the centre and B E as the radius, construct an arc cutting D C produced at F . Hence, 10 . 5 is represented by point F on the number line.

E M B I B E

Secondary School Mathematics FOR CLASS 9>Number Systems>Chapter 1 - Number Systems>EXERCISE 1E

R S Aggarwal and Veena Aggarwal Solutions for Exercise 5: EXERCISE 1E

Author:R S Aggarwal & Veena Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal and Veena Aggarwal Solutions for Exercise 5: EXERCISE 1E

Attempt the free practice questions from Exercise 5: EXERCISE 1E with hints and solutions to strengthen your understanding. Secondary School Mathematics FOR CLASS 9 solutions are prepared by Experienced Embibe Experts.