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 [tex]t = \dfrac{5}{5+2} = \dfrac 5 7[/tex]
[tex]P(\frac 5 7) = \frac 2 7 F + \frac 5 7 H = \left( \dfrac{ 2(-1)+5(-8)}{7}, \dfrac{ 2(-1)+5(20)}{7} \right) = (-42/7, 98/7) = (-6, 14)[/tex]
Answer: (-6, 14)
Plot (-1,-1), (-6,14), (-8,20)
Check out the edge lengths
