Question

given the points a(-3 -5) and b(5,0), find the coordinates off point P that is 2/5 of the way along the directed line segment AB

Answer 1

`((1)/(5), -3)`

Explanation:

The point P is at
`(2)/(5)` of the way along the directed line segment AB.

So, If segment AB = x units then P will be at
`(2x)/(5)` distance from A along AB direction.

That means point P divides the line segment AB in the ratio
`(2x)/(5) : (x - (2x)/(5))` ≡
`(2x)/(5) : (3x)/(5)` ≡ 2 : 3 internally.

If point A is (-3,-5) and point B is (5,0) then the coordinates of point P will be given by
`((-3 * 3 + 5 * 2)/(2 + 3),(-5 * 3 + 0 * 2)/(2 + 3) ) = ((1)/(5), -3)` (Answer)

We know the formula for the coordinates of any point that divide the line segment between the given two point (
`x_(1), y_(1)`) and (
`x_(2), y_(2)`) in the ratio m : n internally is given by

[
`(x_(1)* n + x_(2) * m  )/(m + n), (y_(1)* n + y_(2) * m  )/(m + n)`].