Question

if Q is mid point of the line segment AB and p is the mid point of AQ then, show that PQ=1/4AB

Answer 1

A.........p.........q...................B AB= Aq+qB..... = Aq+Aq (q is mid point so Aq=qB) AB = 2 Aq AB = 2(Ap+pq) AB = 2(pq+pq) (p is mid point so Ap=pq) AB = 2(2pq) AB = 4 pq AB /4 = pq

Answer 2

Answer:

It is proved that $PQ=\frac{1}{4}AB$.

Step-by-step explanation:

If Q is mid point of the line segment AB, then

$AQ=QB$

The line AB can be written as

$AB=AQ+QB$

$AB=AQ+AQ$                $[AQ=QB]$

$AB=2AQ$

P is the mid point of AQ then,

$AP=PQ$

$AB=2AQ$

$AB=2[AP+PQ]$             $[AQ=AP+PQ]$

$AB=2[2PQ]$                   $[AP=PQ]$

$AB=4PQ$

Divide both sides by 4.

$\frac{1}{4}AB=PQ$

Hence proved that  $PQ=\frac{1}{4}AB$.