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If A₁, A₂, A,, , A, are n points in a plane whose coordinates are (x₁, y₁), (x₂₁ y ₂), (X₂₁ Y₂), (X,Y) respectively. A, A, is bisected in the point G₁; G, A, is divided at G, in the ratio 1:2; G, A, is divided at G, in the ratio 1:3; G, A, at G, in the 1:4 and so on until al the points are exhausted. Show that the coordinates of the final point so obtained are x₁ + x₂ +...+x, and y, + y₂ +...+y, 2

If A₁, A₂, A,, , A, are n points in a plane whose coordinates are (x₁, y₁), (x₂₁ y ₂), (X₂₁ Y₂), (X,Y) respectively. A, A, is bisected in the point G₁; G, A, is divided at G, in the ratio 1:2; G, A, is divided at G, in the ratio 1:3; G, A, at G, in the 1:4 and so on until al the points are exhausted. Show that the coordinates of the final point so obtained are x₁ + x₂ +...+x, and y, + y₂ +...+y, 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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If A₁, A₂, A,, , A, are n points in a plane whose coordinates are (x₁, y₁), (x₂₁ y ₂), (X₂₁ Y₂), (X,Y) respectively. A, A, is bisected in the point G,; G, A, is divided at G₂ in the ratio 1:2; G, A, is divided at G, in the ratio 1:3; G, A, at G, in the 1:4 and so on until all the points are exhausted. Show that the coordinates of the final point so obtained are x₁ + x₂ +...+x, y₁ + y₂ + and n +.....+y₁ n
Transcribed Image Text:If A₁, A₂, A,, , A, are n points in a plane whose coordinates are (x₁, y₁), (x₂₁ y ₂), (X₂₁ Y₂), (X,Y) respectively. A, A, is bisected in the point G,; G, A, is divided at G₂ in the ratio 1:2; G, A, is divided at G, in the ratio 1:3; G, A, at G, in the 1:4 and so on until all the points are exhausted. Show that the coordinates of the final point so obtained are x₁ + x₂ +...+x, y₁ + y₂ + and n +.....+y₁ n
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