i. Draw a number line and take point A at 2.
Draw AB perpendicular to the number line such that AB = 1 unit.
In ∆OAB, m∠OAB = 90°
∴ (OB)\(^2\) = (OA)\(^2\) + (AB)\(^2\) … [Pythagoras theorem]
= (2)\(^2\) + (1)\(^2\)
∴ (OB)\(^2\) = 5
∴ OB = √5 units. … [Taking square root of both sides]
With O as centre and radius equal to OB, draw an arc to intersect the number line at C.
The coordinate of the point C is √5 .
ii. Draw a number line and take point P at 3.
Draw PR perpendicular to the number line such that PR = 1 unit.
In ∆OPR, m∠OPR = 90°
∴ (OR)\(^2\) = (OP\(^2\)) + (PR)\(^2\)… [Pythagoras theorem]
= (3)\(^2\) + (1)\(^2\)
∴ (OR)\(^2\) = 10
∴ OR= √10 units. … [Taking square root of both sides]
With O as centre and radius equal to OR,
draw an are to intersect the number line at Q.
The coordinate of the point Q is √10.
