Question

Let AB be the directed line segment beginning at point A(0,4) and ending at point B(9,8). Find the point P on the line segment that partitions the line segment into the segments AP and PB at a ratio of 1:2.

Answer 1

(3, ~1.3), The Y coordinate is rough

Answer 2

`(3,(16)/(3))`

Explanation:

When a line segment with the end points
`(x_1,y_1)` and
`(x_2,y_2)` is divided by a point in the line segment in the ratio m : n,

Then the coordinates of this point are,

`((mx_2+nx_1)/(m+n), (my_2+ny_1)/(m+n))`

Thus, the coordinates of point P that divides a line segment having end points
`A(0,4)` and
`B(9,8)` in the ratio of 1 : 2,

`((1* 9+2* 0)/(1+2),(1* 8+2* 4)/(1+2))`

`((9)/(3),(16)/(3))`

`(3,(16)/(3))`