Question

find the ratio in which the point P(3/4,5/12) divides the line segment joining the points A(1/2,3/2) and B(2,-5) .

Answer 1

A (1/2  , 3/2)          B(2, -5)
  P(3/4 ,  5/12)     lies on the line AB. (assumed). can also verify.

We need to know if P lies externally on AB or it is between A & B.
    1/2  <   3/4  < 2     and     -5 < 5/12   < 3/2

So  P lies in between A & B.

let the ratio:   AP : PB =  m : (1-m)  ,   m is a fraction.

3/4 = m * 2 + (1-m) * 1/2 = 3m/2  + 1/2 
=>   m = 1/6

Ratio:    1/6 :  5/6   = 1 : 5