Find the coordinates of the points of trisection of the line segment joining (4, -1)
and (-2,-3).
Answers
Let P(x₁, y₁) and Q(x₂, y₂) are the points of trisection of the line segment joining the given points.
- Point P divides AB internally in the ratio 1:2.
→ x₁ = (1×(-2) + 2×4)/3
→ (-2 + 8)/3
→ 6/3
→ 2
→ y₁ = (1×(-3) + 2×(-1))/(1 + 2)
→ (-3 – 2)/3
→ -5/3
Hence,
» P(x₁, y₁) = P(2, -5/3)
- Point Q divides AB internally in the ratio 2:1.
→ x₂ = (2×(-2) + 1×4)/(2 + 1)
→ (-4 + 4)/3
→ 0
→ y₂= (2×(-3) + 1×(-1))/(2 + 1)
→ (-6 – 1)/3
→ -7/3
Hence,
The coordinates of the point Q is (0, -7/3).
Answer:
Let A(4,-1) be the first point and B(-2,-3) be the second point and P and Q be the the internally trisecting point.
Let AB=PQ=QB=k
PB=PQ+QB=2k
and AQ=AP+PQ=2k
>AP:PB=1:2
and AQ:QB=2:1
P divides a b internally in ratio 1:2 while Q divides internally in the ratio 2:1. Does coordinates of p and q are
P{[1×(-2)+2×4]/1+2 , 1×(-3)+2×(-1)]/1+2} = P[2,(-5/3)]
and similarly
Q[0,(-7/3)]