Let's say we seek P between K and L such that
KP:PL = 3:2
P is a bit closer to L; knowing that helps us keep our fractions straight.
The line from K to L parametrically is
(x,y) = (1-t)K + tL = K + t(L-K)
t=0 means right on K, and t=1 means right on L.
We want t = 3/(3+2) = 3/5, which is in the right proportion, closer to L
K(-5,-4) to L(5,1)
P(x,y) = K + (3/5)(L - K) = (-5,-4) + (3/5)(5 - -5, 1 - -4) = (-5,-4)+(6,3) = (1, -1)
Let's check the coordinates separately; they should match:
KPx:PLx = (1- -5):(5 -1) = 6:4 = 3:2, good
KPy:PLy = (-1 - -4) : ( 1 - -1 ) = 3:2, good
Answer: (1, -1)
