﻿                  A1, A2, A3, …. An are n points in a plane whose coordinates are (x1, y1), (x2, y2), (x3, y3) …, (xn, yn) respectively A1, A2 is dissected at the point G1, G1 A3 is divided in the ratio  1 : 2 at G2, G2 A4 is divided in the ratio 1 : 4 at G4, and so on until all n points are exhausted. The coordinates of the final point G so obtained are : Kaysons Education

# A1, A2, A3, …. An Are n points In A Plane Whose Coordinates Are (x1, y1), (x2, y2), (x3, y3) …, (xn, yn) Respectively A1, A2 is Dissected At The Point G1, G1 A3 is Divided In The Ratio  1 : 2 At G2, G2 A4 is Divided In The Ratio 1 : 4 At G4, And So On Until All n points Are Exhausted. The Coordinates Of The Final Point G so Obtained Are

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## Question

### Solution

Correct option is

The coordinates of G1 are

Now, G2 divides G1A3 in the ratio 1: 2. Therefore, the coordinates of G2are

or

Again, G3 divides G2A4 in the ratio 1: 3. Therefore, the coordinates ofG2 are

or

Proceeding in this manner, we can show that the coordinates of the final point G so obtained will be

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