`A, B, C, D...` are n points in a plane whose coordinates are `(x_1, y_1), (x_2, y_2), (x_3, y_3), ... AB` is bisected in the point `G_1;G_1C` is divided at `G_2` in the ratio `1:2; G_2 D` is divided at `G_3` in the ratio `1:3; G_3E` at `G_4` in the ratio `1:4,` and so on until all the points are exhausted. Shew that the coordinates of the final point so obtained are, `(x_1+x_2+x_3+......+x_n)/n and (y_1+y_2+y_3+.....+yn)/n`

If A_(1),A_(2),A_(3),…,A_(n) are n points in a plane whose coordinates are (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)),…,(x_(n),y_(n)) respectively. A_(1)A_(2) is bisected in the point G_(1) : G_(1)A_(3) is divided at G_(2) in the ratio 1 : 2, G_(2)A_(4) at G_(3) in the1 : 3 and so on untill all the points are exhausted. Show that the coordinates of the final point so obtained are (x_(1)+x_(2)+.....+ x_(n))/(n) and (y_(1)+y_(2)+.....+ y_(n))/(n)

If A_(1),A_(2),A_(3),…,A_(n) are n points in a plane whose coordinates are (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)),…,(x_(n),y_(n)) respectively. A_(1)A_(2) is bisected in the point G_(1) : G_(1)A_(3) is divided at G_(2) in the ratio 1 : 2, G_(3)A_(5) at G_(4) in the1 : 4 and so on untill all the points are exhausted. Show that the coordinates of the final point so obtained are (x_(1)+x_(2)+.....+ x_(n))/(n) and (y_(1)+y_(2)+.....+ y_(n))/(n)

If A_(1),A_(2),A_(3),…,A_(n) are n points in a plane whose coordinates are (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)),…,(x_(n),y_(n)) respectively. A_(1)A_(2) is bisected in the point G_(1) : G_(1)A_(3) is divided at G_(2) in the ratio 1 : 2, G_(3)A_(5) at G_(4) in the1 : 4 and so on untill all the points are exhausted. Show that the coordinates of the final point so obtained are (x_(1)+x_(2)+.....+ x_(n))/(n) and (y_(1)+y_(2)+.....+ y_(n))/(n)

Let A_1,A_2,A_3,...,A_n are n Points in a plane whose coordinates are (x_1,y_1),(x_2,y_2),....,(x_n,y_n) respectively. A_1A_2 is bisected at the point P_1,P_1A_3 is divided in the ratio 1:2 at P_2,P_2A_4 is divided in the ratio 1:3 at P_3,P_3A_5 is divided in the ratio 1:4 at P_4 and the so on until all n points are exhausted. find the coordinates of the final point so obtained.

Given that A_1,A_2,A_3, A_n are n points in a plane whose coordinates are x_1,y_1),(x_2,y_2) ,(x_n ,y_n), respectively. A_1A_2 is bisected at the point P_1,P_1A_3 is divided in the ratio A :2 at P_2,P_2A_4 is divided in the ratio 1:3 at P_3,P_3A_5 is divided in the ratio 1:4 at P_4 , and so on until all n points are exhausted. Find the final point so obtained.

Given that A_1,A_2,A_3, A_n are n points in a plane whose coordinates are x_1,y_1),(x_2,y_2) ,(x_n ,y_n), respectively. A_1A_2 is bisected at the point P_1,P_1A_3 is divided in the ratio A :2 at P_2,P_2A_4 is divided in the ratio 1:3 at P_3,P_3A_5 is divided in the ratio 1:4 at P_4 , and so on until all n points are exhausted. Find the final point so obtained.

Given that A_1,A_2,A_3, A_n are n points in a plane whose coordinates are x_1,y_1),(x_2,y_2) ,(x_n ,y_n), respectively. A_1A_2 is bisected at the point P_1,P_1A_3 is divided in the ratio A :2 at P_2,P_2A_4 is divided in the ratio 1:3 at P_3,P_3A_5 is divided in the ratio 1:4 at P_4 , and so on until all n points are exhausted. Find the final point so obtained.

The point whose coordinates are x=x_(1)+t(x_(2)-x_(1)), y=y_(1)+t(y_(2)-y_(1)) divides the join of (x, y) and (x_(2), y_(2)) in the ratio