Question

Given segment AB with points (-4, 8) and (6, 3) respectively. Find the coordinates of point P that partitions Segment AB in the ratio 3:2. The answer should be entered in the form (x,y) with out any spaces between characters.

Answer 1

`P = (2,5)`

Explanation:

Given

`A(-4,8)`

`B(6,3)`

`m:n = 3 : 2`

Required

Determine P

Since P divides the segment into 3:2, P is calculated using

`P = ((nx_1 +m x_2)/(m+n),(ny_1 + my_2)/(m+n))`

Where

`(x_1,y_1) = (-4,8)`

`(x_2,y_2) = (6,3)`

`m:n = 3 : 2`

Substitute these values in the above formula:

`P = ((2 * -4 +3 * 6)/(3 + 2),(2 * 8 + 3 * 3)/(3 + 2))`

`P = ((-8 +18)/(3 + 2),(16 + 9)/(3 + 2))`

`P = ((10)/(5),(25)/(5))`

`P = (2,5)`