Lines Divided in ratio

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 G4 in the ratio 1:4..and so on untill all the points are exhausted..Find the coordinates of final point?

1 Answers

Shaswata Roy ·

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,Gn-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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