Question

what is the Y-cordinate of the point that divides the directed line segment from J to K into the ratio of 2:3​

Answer 1

We can represent the segment parametrically:

`P(t) = (1-t)J + tK`

When t=0 we get P=J, when t=1 we get P=K. So when P is between J and K,

`PJ/PK = t/(1-t)`

We want the point P so that

PJ/PL=2/3

That's

`t/(1-t) = 2/3`

`3t = 2 - 2t`

`5t = 2`

`t = 2/5`

That means 2/5ths along the way from J to K, which we could have gotten immediately as 2/(2+3).

`P = (1 - \frac 2 5)J + \frac 2 5 K = \frac 3 5 (-3, 1) + \frac 2 5(-8,11)`

We're only after the y coordinate,

`P_y = \frac 3 5 (1) + \frac 2 5(11) = (25)/(5) = 5`

Answer: 5