Question

if the point P(2,1) lies on the line segment joining the points A(4,2) and B(8,4) then find AP/PB

Answer 1

A ==========P ==============B

A(4 , 2) B(8 , 4) and P (2,1)

use section formula ,
let PA : PB =m : n

then,
2 ={8 × m + 4 × n}/(m + n)

2(m + n) =(8m + 4n)

2m +2n =8m + 4n

-6m = 2n

m/n = 1 : -3

here negative sign means p externally divided of AB .

Answer 2

A(4 , 2) B(8 , 4) and P (2,1)use section formula ,let PA : PB =m : n then,
2 ={8 × m + 4 × n}/(m + n)
2(m + n) =(8m + 4n)
2m +2n =8m + 4n
-6m = 2n
m/n = 1 : -3