We can represent the segment parametrically:
[tex]P(t) = (1-t)J + tK[/tex]
When t=0 we get P=J, when t=1 we get P=K. So when P is between J and K,
[tex]PJ/PK = t/(1-t)[/tex]
We want the point P so that
PJ/PL=2/3
That's
[tex]t/(1-t) = 2/3[/tex]
[tex]3t = 2 - 2t[/tex]
[tex]5t = 2[/tex]
[tex]t = 2/5[/tex]
That means 2/5ths along the way from J to K, which we could have gotten immediately as 2/(2+3).
[tex]P = (1 - \frac 2 5)J + \frac 2 5 K = \frac 3 5 (-3, 1) + \frac 2 5(-8,11)[/tex]
We're only after the y coordinate,
[tex]P_y = \frac 3 5 (1) + \frac 2 5(11) = \frac{25}{5} = 5[/tex]
Answer: 5
