An unending sequence of points!

Geometry Level 4

$A_i$ (where $i \in \left\{ 1,2,3,4, \cdots ,n \right\}$ ) are $n$ points in a plane whose coordinates are denoted by $\left( x_i , y_i \right)$ respectively.

$A_1 A_2$ is divided in the ration of $1:1$ at $G_1$
$G_1 A_3$ is divided in the ratio of $1:2$ at $G_2$
$G_2 A_4$ is divided in the ratio of $1:3$ at $G_3$
This process continues until
$G_{n-1} A_{k_n}$ is divided in the ratio $1:n$ at $G_n$

What are the coordiantes of $G_n$ ?

\left(\frac{\displaystyle\sum_{i=1}^n x_i}{n-1},\frac{\displaystyle\sum_{i=1}^n y_i}{n-1}\right)

\left( \displaystyle \sum_{i=1}^n x_i , \displaystyle \sum_{i=1}^n y_i \right)

\left(\dfrac{\displaystyle\sum_{i=1}^n x_i}{n} , \dfrac{\displaystyle\sum_{i=1}^n y_i}{n}\right)

\left(\frac{\displaystyle\sum_{i=1}^n x_i}{n+1},\frac{\displaystyle\sum_{i=1}^n y_i}{n+1}\right)

1 solution

Krishnaraj Sambath
Sep 13, 2019

I cheated. Put n = 2. Only one of the options was a logical outcome..

An unending sequence of points!

1 solution

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