Question

Find the co-ordinates of the points which trisects the line segment joining (0,-5) and (-3,4)​ .
​

Answer 1

Answer:

Let A(1, -2) and B(-3, 4) be the

given points.

Let the points of trisection be

P and Q. Then AP = PQ = QB = λ (say)

∴ PB = PQ + QB = 2λ and AQ = AP + PQ = 2λ

⇒ AP : PB = λ:2λ=1:2 and AQ : QB = λ:2λ=2:1

So,

P divides AB internally in the ratio 1 : 2 while Q divides internally in the ratio 2 : 1

∴ the co-ordinates of P are (1+21×−3+2×1,1+21×4+2×−2)or(−31,0)

and the co-ordinates of Q are (2+12×−3+1×1,2+12×4+1×(−2))or(−35,2)

Hence,

the points of trisection are (−31,0)and(−35,2)