Question

Find the point of trisection of the line segment joining the points (1, 2) and (11,9).
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Answer 1

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+2

1×−3+2×1

,

1+2

1×4+2×−2

)or(−

3

1

,0)

and the co-ordinates of Q are (

2+1

2×−3+1×1

,

2+1

2×4+1×(−2)

)or(−

3

5

,2)

Hence, the points of trisection are (−

3

1

,0)and(−

3

5

,2)