A(1,1) and B(2,-3) are two points and D is a point on AB produced such that AD=3AB. Find the co-ordinates of D

Dear Chanchal ,

we are given AD =3AB , AB +BD  = 3AB ;  2AB = BD , therefore B divides AD in the ratio of 1:2.

let d be (x,y ) then applying formulae ,

   2  = (x +2)/3 ;  x = 4 and -3 = (y +2)/3 =-3 ; y =-11

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ans    let D(x,y)

           let AB=k and AD= 3k

           x=3k(2)+k(1)/4k = 6k+k/4k = 7/4.

           y=3k(-3)+k(1)/4k = -9k+k/4k = -2.

   HENCE D(7/4,-2).