Question

Find the ratio in which the poin `P(3/4, 5/12)` divides the line segment joining the points `A(1/2, 3/2)` and B(2, –5).

Answer 1

`"Let  k : 1 be 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).` Then 

`(3/4 , 5/12) = ((k(2)+1/2)/(k+1) , (k(-5)+2/2)/(k+1))`

` ⇒(k (2) +1/2)/(k+1) = 3/4  and  (k(-5) +3/2) /(k+1) = 5/12`

`⇒ 8k+2=3k+3 and -60k +18 = 5k +5`

`⇒k=1/5 and k = 1/5 `
Hence, the required ratio is1:5