Question

What are the coordinates of the point on the directed line segment from (-3, -9) to (4,5)

Answer 1

(2, 1 )

Explanation:

Using the Section formula

For endpoints (x₁, y₁ ) and (x₂, y₂ ) partitioned in the ratio m : n

Then coordinates of point are

[
`(mx_(2)+nx_(1) )/(m+n)` ,
`(my_(2)+ny_(1) )/(m+n)` ]

Here m = 5, n = 2, (x₁, y₁ ) = (- 3, - 9), (x₂, y₂ ) = (4, 5), thus partitioned point

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

= [
`(20-6)/(7)` ,
`(25-18)/(7)` ]

= (
`(14)/(7)` ,
`(7)/(7)` )

= (2, 1 )