Question

If Q is midpoint of line segment AB and P is midpoint 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:

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

Step-by-step explanation:

We are given that Q is midpoint of line segment AB

Mid point divides the line into two equal parts

So, $AQ= QB = \frac{1}{2}AB$  --- 1

Now P is midpoint of AQ

P divides the line AQ into two equal parts

So, $AP = PQ = \frac{1}{2}AQ$

Using 1

$AP = PQ = \frac{1}{2} \times \frac{1}{2} AB$

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

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