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Find the Coordinates of Points Which Trisect the Line Segment Joining (1, –2) and (–3, 4) - CBSE Class 10 - Mathematics

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Question

Find the coordinates of points which trisect the line segment joining (1, –2) and (–3, 4)

Solution

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 = 2λ : λ = 2 : 1

So, P divides AB internally in the ratio 1 : 2 while Q divides internally in the ratio 2 : 1. Thus, the coordinates of P and Q are

`P( \frac{1\times (-3)+2\times 1}{1+2},\ \frac{1\times 4+2\times (-2)}{1+2})=P( \frac{-1}{3},\ 0)`

`Q( \frac{2\times (-3)+1\times 1}{2+1},\ \frac{2\times 4+1\times (-2)}{2+1})=Q( \frac{-5}{3},\ 2)" respectively"`

Hence, the two points of trisection are (–1/3, 0) and (–5/3, 2).

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Solution Find the Coordinates of Points Which Trisect the Line Segment Joining (1, –2) and (–3, 4) Concept: Section Formula.
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