Question

What are the cordinates of the point on the directed line segment from -3 -9 to 4 5 that partitions the segment into a ratio of 5 to 2

Answer 1

`(x,y) = (2,1)`

Explanation:

Given

Coordinate: (-3,-9) and (4,5)

Ratio= 5 : 2

Required

Determine the point at the segment

The coordinate of the point is calculated using:

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

Where:

`m : n=5:2`

`(x_1,y_1) = (-3,-9)`

`(x_2,y_2) = (4,5)`

So, we have:

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

`(x,y) = [(5 * 4 + 2 * -3)/(5+2),(5*5+2*-9)/(5+2)]`

`(x,y) = [(14)/(7),(7)/(7)]`

`(x,y) = (2,1)`

The coordinate of the point is: (2,1)