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.

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)

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

Find the coordinates of the point which divides the join of the points P(5,4,-2) and Q(-1,-2,4) in the ratio 2:3

The line segment joining the points A(3,2) and B (5,1) is divided at the point P in the ratio 1 : 2 and it lies on the line 3x-18y+k=0 . Find the value of k.

The coordinates of the point P dividing the line segment joining the points A(1, 3) and B(4, 6) in the ratio 2:1 is

The coordinates of a point which divide the line joining the points P(2,3,1) and Q(5,0,4) in the ratio 1:2 are

A point P on the x-axis divides the line segment joining the points (4, 5) and (1, -3) in certain ratio . Find the co-ordinates of point P.