Question

If PQ is the perpendicular bisector of line segment AB then the length of PQ will be.

• A. always equals to AB
• B. never equals to AB
• C. may be equals to AB

Answer 1

The correct option is C may be equals to AB


In above diagram, If OP = $\frac{1}{2}$AB
then

$AP=\sqrt{A{O}^2+O{P}^2}$

$⟹AP=\sqrt{(\frac{1}{2}AB{)}^2+(\frac{1}{2}AB{)}^2}$
(As AO = OP = $\frac{1}{2}$AB)

$⟹AP=\frac{AB}{\sqrt{2}}>\frac{1}{2}AB$

Now, If PQ = AB, $AP=\frac{AB}{\sqrt{2}}>\frac{1}{2}AB$. Hence perpendicular bisector can be drawn. Therefore, PQ may be equals to AB.