Lines Divided in ratio

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A,B,C,D....... are 'n' points in a plane whose coordinates are (x₁,y₁),(x₂,y₂),(x₃,y₃)..........AB is bisected in the point G₁..G₁C is divided at G₂ in the ratio 1:2 ..G₂D is divided at G₃ in the ratio 1:3..G₃E at G₄in the ratio 1:4..and so on untill all the points are exhausted..Find the coordinates of final point?

#Mathematics #Co-ordinate Geometry

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Shaswata Roy ·2013-10-10 09:07:15

Coordinates of G₁=\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)

Coordinates of G₂=\left(\frac{2\times\frac{x_{1}+x_{2}}{2}+x_{3}}{3},\frac{2\times\frac{y_{1}+y_{2}}{2}+y_{3}}{3}\right)=\left(\frac{x_{1}+x_{2}+x_{3}}{3},\frac{y_{1}+y_{2}+y_{3}}{3}\right)

Proceeding in this manner,G_n-1 turns out to be

\left(\frac{x_{1}+x_{2}+x_{3}+\cdots +x_{n}}{n},\frac{y_{1}+y_{2}+y_{3}+\cdots +y_{n}}{n}\right)

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° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

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Lines Divided in ratio

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