Find the co-ordinates of the point R, which divides [PQ] externally in the ratio 2: 1 and verify that Q is the mid-point of PR.

Find the coordinates of a point which divides externally the line joining (1, -3) and (-3, 9) in the ratio 1 : 3.

Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2 :3.

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

Find the co-ordinates of the point A which divides the line segment joining :- P (5,- 2) and Q (9, 6) in the ratio 3 : 1.

Find the co-ordinates of the point, which divides the line segment joining the points (5, 4, 2) and (-1, -2, 4) in the ratio : 2:3 .

Find the co-ordinates of the points, which divide the join of the points (1, -2, 3) and (3, 4, -5) in the ratio 2 : 3 internally.

Find the co-ordinates of the point, which divides the join of (-2, 3, 5) and (1, - 4, - 6) in the ratio 2 : 3 internally.

A point R with x-coordinate 4 lies on the line segment joining the points P(2, -3, 4) and Q (8, 0, 10). Find the coordinates of the point R. [Hint Suppose R divides PQ in the ratio k :1. The coordinates of the point R are given by ((8k+2)/(k+1), (-3)/(k+1), (10k+4)/(k+1)) .

Find the coordinates of the point which divides the line segment joining the points A(5,-2) and B(9,6) in the ratio 3:1