Discussion Forum



1)

M and N  are the mid-points of the diagonals Ac and BD  respectively of quandrilateral ABCD , then AB+AD+CB+CD is equal to


A) 2MN

B) 2NM

C) 4MN

D) 4NM

Answer:

Option C

Explanation:

Let the position vectors of A, B, C, D, M  and N are a,b, c,d  , m and n

Since , M and N are the mid-points of AC  and BD

$\therefore$   m= $\frac{a+c}{2}$, n= $\frac{b+d}{2}$

Now, AB+AD+CB+CD

=(b-a)+(d-a)+(b-c)+(d-c)

=2(b+d)-2(a+c)

=2 x 2n-2 x 2 m

=4(n-m)=4MN