Question

Line segment RS is the directed line segment from R(-6,-5) to S(4,0). What are the coordinates of the point that partitions the segment in the ratio 2:3?

Answer 1

`(x,y) = (-2,-3)`

Explanation:

Given

`R = (-6,-5)`

`S = (4,0)`

`Ratio = 2:3`

Required

Determine the coordinate of the line ratio

Line ratio is calculated using:

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

In this case

`(x_1,y_1) = (-6,-5)`

`(x_2,y_2) = (4,0)`

`m:n = 2:3`

The formula becomes:

`(x,y) = ((2 * 4 + 3 * -6)/(2+3),(2 * 0 + 3 * -5)/(2+3))`

`(x,y) = ((8 - 18)/(5),(0 - 15)/(5))`

`(x,y) = ((-10)/(5),(-15)/(5))`

`(x,y) = (-2,-3)`