What are the coordinates of the point on the directed line segment from ( − 8 , 10 ) (−8,10) to ( − 8 , − 5 ) (−8,−5) that partitions the segment into a ratio of 2 to 1?

Answer 1

If the endpoints of a line segment are (a,c) and (b,d) and p is a fraction greater than 0 and less than or equal to 1, then the point which divides the segment into 2 segments in the ratio p:(1-p) has co-ordinates

[a(1-p)+bp,c(1-p)+dp]. In your problem p=2/3.