Question

If A (2 , 7), B (-4, -8) are given, find the co-ordinates of the points of trisection of segment AB.​

Answer 1

Answer:

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Step-by-step explanation:

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=2λandAQ=AP+PQ=2λ

⇒AP:PB=λ:2λ=1:2andAQ: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(

1+2

1×−3+2×1

,

1+2

1×4+2×−2

)=P(

3

−1

,0)

Q(

2+1

2×−3+1×1

,

2+1

2×4+1×(−2)

)=Q(

3

−5

,2)respectively

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

REMARK: As Q is the mid-point of BP. So, the coordinates of Q can also be obtained by using mid-point formula.