Locate 2 on the number line. Class 9

Locate 2 on the number line. Class 9

Question 1.

Locate [latex]\sqrt{2}[/latex] on the number line. Class 9

Solution:

Step 1:

On the number line, mark point O as 0 and point A such that OA = 1 unit.

Draw a perpendicular to OA through A.

Step 2:

On the perpendicular line, mark a point B such that AB = 1 unit.

Join O to B.

Then, ∆OAB is a right triangle.

Using the Baudhayana-Pythagoras Theorem,

$\begin{aligned} \mathrm{OB} & =\sqrt{\mathrm{OA}^2+\mathrm{AB}^2} \\ & =\sqrt{1^2+1^2}=\sqrt{2} \text { units }\end{aligned}$

Step 3:

With O as centre and OB as radius, with a compass draw an arc cutting the number line at point P.

Then, OP = [latex]\sqrt{2}[/latex] units

Hence, point P represents [latex]\sqrt{2}[/latex] on the number line.