Mathematics: What is the y-cordinate of the point that divides the directed line segment from j to k into the ratio of 2: 3

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What is the y-cordinate of the point that divides

SumayahAminaAnsari

17.01.2022

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,

$P_y = \frac 3 5 (1) + \frac 2 5(11) = \frac{25}{5} = 5$

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