Question

Find the coordinated if point G that lies along the directed line segment from F(-1,-1) to H(-8,20) and partitions the segment in the ratio of 5:2

Answer 1

The parametric segment between F and H is

P(t) = (1-t)F + tH

P(0)=F, P(1)=H.

We want P such that FP:PH=5:2

That corresponds to
`t = (5)/(5+2) = \frac 5 7`

`P(\frac 5 7) = \frac 2 7 F + \frac 5 7 H = \left( ( 2(-1)+5(-8))/(7), ( 2(-1)+5(20))/(7) \right) = (-42/7, 98/7) = (-6, 14)`

Answer: (-6, 14)

Plot (-1,-1), (-6,14), (-8,20)

Check out the edge lengths