Question

Line segment RW has endpoints R(-4,5) and W(6,20). Point P is on RW such that RP:PW is 2:3. What are the coordinates of point P?

Answer 1

The coordinates of P are (0,11).

Explanation:

Since, when a point divides a line segment in the ratio of m : n that having endpoints
`(x_1,y_1)` and
`(x_2,y_2)` and lies between these points.

Then, the coordinates of the point are,

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

Hence, the coordinates of point P that divides the Line segment RW has endpoints R(-4,5) and W(6,20) in 2:3 ratio are,

`((2(6)+3(-4))/(2+3),(2(20)+3(5))/(2+3))`

`=((12-12)/(5),(40+15)/(5))`

`=(0,(55)/(5))`

`=(0,11)`