1.

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

Answer»

2 MN
2NM
4 MN
4 NM

Solution :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=(a+c)/(2),n=(b+d)/(2)`
Now, `AB+AD+CD+CD`
`=(b-a)+(d-a)+(b-c)+(d-c)`
`=2(b+d)-2)a+c)`
`=2xx2n-2xx2m`
`=4 (n-m)=4 NM`


Discussion

No Comment Found

Related InterviewSolutions