Let `square PQRS` be a quadrilateral. If M and N are the mid-points of the sides PQ and RS respectively, then PS+QR=

Options

A. `3MN`
B. `4 MN`
C. `2 MN`
D. `2 NM`

Answer

C

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 respetively of quadrilateral PQRS .
`m = (p + q)/(2)` and `n = (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`