Choose whether the given statement is true or false.
is not on the number line.

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True

False

answer is B.

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Detailed Solution

Let us take

and represent it on the number line.
To represent the number

, we require the Pythagoras theorem.
According to the Pythagoras theorem, we know that

--------------------(1)
We have to take the measure of the hypotenuse equal to

units.
Now, taking 3 units as the base OA on the x-axis and a perpendicular BA of length 1 unit on that base.
Question Image

Plotting OA = 3 units on the number line and the perpendicular BA = 1 unit, we get
Question Image

In the ΔBAO, we have
Perpendicular = BA = 1 unit …………………………………….(2)
Base = OA = 3 units ……………………………………….(3)
From equation (1), we have

From equation (2) and equation (3), we have the lengths of the base and the perpendicular.
On putting, Perpendicular = BA = 1 unit and Base = OA = 3 units in equation (1), we get
Question Image

Now, take OB as a radius and draw an arc intersecting the real axis that is our x-axis at C.
Since

is an arc that is drawn by taking O as the center, we can say that the lengths OB and OC are equal because all the radius of an arc are equal to each other.
Question Image

Therefore,

.
Here, OC represents the number

on the real number line.
Since, It is false.
The correct statement is: “

is on the number line.”

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