Discussion Forum

Let $\Box$ PQRS  be a quadrilateral , if M and N are the mid-points of the sides PQ and RS respectively , then PS+QR=

Answer:

Explanation:

Let p,q, r, s , m and n be the position vectors of P.Q,R,S,M and N be respectively.

Given ,M and N are the mid-points of PQ and RS respectively of quadrilateral PQRS

 $m=\frac{p+q}{2}$  and $n=\frac{p+s}{2}$   .......(i)

Now, PS QR = (PV of S- PV of P)+(PV of R-PV of Q)

 = s+p+r-q

 =(r+s)-(p+q)

=2n-2m     [from Eq.(i)]

=2(n-m)=2MN