State if the statement is true or false: The representation of

6

and

7

on the real number line is

Question

State if the statement is true or false: The representation of

6

and

7

on the real number line is

Accepted Answer

We have to find if the given representation of

6

and

7

is true or not.To represent

6

and

7

on the number line, we have to represent

5

first. To do so, mark a point 2 units away from the starting point, i.e., 0, and then draw a perpendicular on that line, of 1 unit. Next, join the initial point with the free end of the perpendicular to form a triangle as shown below.Applying Pythagoras theorem on the above triangle, we get the length of the hypotenuse as follows,

a
      2
     
     +
      b
      2
     
     =
      c
      2

2
      2
     
     +
      1
      2
     
     =
      c
      2

c
      2
     
     =5

c=
      5

Now, taking the hypotenuse as the radius and the initial point as the center, draw an arc that intersects the number line. The point where it intersects is

5

, as shown above in the diagram.Next, to represent

6

on the number line, repeat the same procedure as for

5

, i.e., on the same triangle, considering the hypotenuse as the base, draw a perpendicular line of 1 unit and join it to the initial point as shown below.Applying the Pythagoras theorem on the second triangle, we get,

a
      2
     
     +
      b
      2
     
     =
      c
      2

(
       5
      
      )
      2
     
     +
      1
      2
     
     =
      c
      2

c
      2
     
     =5+1

c=
      6

Now, taking the second hypotenuse as the radius and the initial point as the center, draw an arc that intersects the number line. The point where it intersects is

6

, as shown above in the diagram.Again, for representing

7

, again, repeat the same procedure as for

6

, i.e., on the second triangle, considering the hypotenuse as the base, draw a perpendicular line of 1 unit and join it to the initial point as shown below.Applying the Pythagoras theorem on the third triangle, we get,

a
      2
     
     +
      b
      2
     
     =
      c
      2

(
       6
      
      )
      2
     
     +
      1
      2
     
     =
      c
      2

c
      2
     
     =6+1

c=
      7

Now, taking the third hypotenuse as the radius and the initial point as the center, draw an arc that intersects the number line. The point where it intersects is

7

, as shown above in the diagram.In this way,

6

and

7

can be represented on a real number line and so, the given representation is correct.Hence, the statement is true.So, the correct option is 1.

State if the statement is true or false: The representation of $6$ and $7$ on the real number line is

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