Question

Find the co-ordinates of the points which trisect the line segment joining (1,-2) and (-3,4)

Answer 1

Answer:

Step-by-step explanation:

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 upon-3,0)

and the co-ordinates of Q are (-5 upon -3,2)

Hence, the points of trisection are ( -1 upon-3,0),(-5 upon -3,2)