Point A is located at (5, 6) and point B is located at (8, −2) .

What are the coordinates of the point that partitions the directed line segment AB¯¯¯¯¯ in a 1:3 ratio?

What we are looking for is the point that is 1 / (1 + 3) = 1/4 the distance from A to B

This can be calculated as follows :

[ 5 + (8 - 5)/4 , 6 + (-2 - 6)/4 ] =

[ 5 + 3/4 , 6 + -8/4 ]

[ 5 + 3/4, 6 - 2 ]

( 23/4, 4 )

@CPhill can we just find the midpoint and divide the answer by 4??

I didn't think of that approach...but.....we want to find the midpoint of AB and then find the midpoint of A to this calculated midpoint