
Locate on the number line.
Answer
521.7k+ views
Hint: In this question we will use the methods of representing a number on number line. Every real number is represented by a unique point on the number line. Also every point on the number line represents a unique real number. We will locate a number on the number line by using Pythagoras theorem.
Complete step-by-step solution:
Here , we have to locate on number line,
We will do this by using the Pythagoras theorem.
Here, we can write as:
…….(i)
We know that , according to Pythagoras theorem ,
(hypotenuse) = .
By comparing this with equation (i) ,we get
Hypotenuse = , perpendicular = 1 and base = 3.
Now, according to this, the steps of construction are as follows :
Step 1. : Take a line segment PO =3 units on the x –axis. (consider 1 unit =2 cm) .
Step 2: Draw a perpendicular on O and draw a line OQ = 1 unit.
Step 3: Now join PQ with .
Step 4: Take P as centre and PQ as radius, draw an arc which cuts the x- axis at point E.
Step 5: Now the line segment PQ in the figure represents units .
Hence, through these steps we had located on the number line.
Note: In this type of question we should remember some basic points like we should know Pythagoras theorem and basic knowledge of number line and then by using the Pythagoras theorem we will find out the things like hypotenuse, perpendicular and base. Hence by doing step by step construction, we will locate the given number on the number line.
Complete step-by-step solution:
Here , we have to locate
We will do this by using the Pythagoras theorem.
Here, we can write
We know that , according to Pythagoras theorem ,
By comparing this with equation (i) ,we get
Hypotenuse =
Now, according to this, the steps of construction are as follows :
Step 1. : Take a line segment PO =3 units on the x –axis. (consider 1 unit =2 cm) .
Step 2: Draw a perpendicular on O and draw a line OQ = 1 unit.
Step 3: Now join PQ with
Step 4: Take P as centre and PQ as radius, draw an arc which cuts the x- axis at point E.
Step 5: Now the line segment PQ in the figure represents
Hence, through these steps we had located

Note: In this type of question we should remember some basic points like we should know Pythagoras theorem and basic knowledge of number line and then by using the Pythagoras theorem we will find out the things like hypotenuse, perpendicular and base. Hence by doing step by step construction, we will locate the given number on the number line.
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