SOLUTION: If A(-10, -4) and B(5,16), find the coordinates of P(x,y) that divides AB such that AP:PB=2:3.

Algebra ->  Finance -> SOLUTION: If A(-10, -4) and B(5,16), find the coordinates of P(x,y) that divides AB such that AP:PB=2:3.      Log On


   

Question 1012381: If A(-10, -4) and B(5,16), find the coordinates of P(x,y) that divides AB such that AP:PB=2:3.
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
AP/PB = 2/3 +> p-a/b-p = 2/3
Cross multiply
2(b - p) = 3(p - a)
2b - 2p = 3p - 3a
Collect like terms
-2p - 3p = -3a - 2b
-5p = -3a - 2b
Multiply both sides by -1
5p = 3a + 2b
p = 1/5(3a + 2b)
p = 1/5(3{-10, -4} + 2{5, 16})
p = 1/5{-30, -12} + {10, 32}
p = 1/5[-20, 20]
p = [-4, 4]
Hope this helps :-)