`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_(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)

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.

Find the ratio in which the join the A(2,1,5) and B(3,4,3) is divided by the plane 2x+2y-2z=1. Also find the coordinates of the point of division.

Find the ratio in which the line joining the points (1, 3, 2), and (-2, 3, -4) is divided by the YZ-plane. Also, find the coordinates of the point of division.

A point C divides the line AC, where A(1, 3) and B(2, 7) in the ratio of 3:4 . The coordinates of C are

The line segment joining points (2, -3) and (-4, 6) is divided by a point in the ratio 1: 2. Find the coordinates of the point.

The line segment joining the points (-3,-4), and (1,-2) is divided by y-axis in the ratio a. 1:3 b. 2:3 c. 3:1 d. 3:2