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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 G4 in the ratio 1:4, and so on until all the points arr exhausted. Show that the coordinate of the final point so obtained are x1+x2+x3+...+xn/n and y1+y2+y3+...yn/n

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 until all the points arr exhausted. Show that the coordinate of the final point so obtained are x1+x2+x3+...+xn/n and y1+y2+y3+...yn/n

Grade:11

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