Question

What are the coordinates of the point on the directed line segment from (5,5) to

(8,-4) that partitions the segment into a ratio of 1 to 2?

Answer 1

`(x,y) = (6,2)`

Explanation:

Given

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

`(x_2,y_2) = (8,-4)`

`m:n = 1:2`

Required

Determine the coordinate of the partition

This is calculated using:

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

Substitute values for m,n,x's and y's

`(x,y) = ((1 * 8 + 2 * 5)/(1+2),(1*-4 + 2*5)/(1 + 2))`

`(x,y) = ((18)/(3),(6)/(3))`

`(x,y) = (6,2)`