In quadrilateral (A B C D, A B = a , B C = b ), ( A D = b - a ) if (M ) is the midpoint of (B C ) and (N ) is a point on (D M ) such that (D N= ( 4 5 ) D M ), then (5 A N = )

Step-by-step solution

It is given that for a quadrilateral (A B C D ), ( A B = a , B C = b , A D = b - a ) ( ) According to the question, ( B M = b 2 ) and ( aligned & D N N M = 4 1 D N= ( 4 5 ) D M given & A N - A D = 4 1 ( A M - A N ) & 5 AN =4 A M + A D =4 ( a + b 2 )+( b - a ) & =4 a +2 b + b - a =3( a + b )=3 A C aligned ) Hence, option (c) is correct.