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

`1:5`

Explanation

Let the required ratio be k: 1.
Then, the coordinates of P are `((2k + (1)/(2))/(k+1), (-5k + (3)/(2))/(k+1))`.
`therefore (2k + (1)/(2))/(k +1) = (3)/(4) rArr (4k+1)/(2(k+1)) = (3)/(4) rArr 16k + 4 = 6k +6`
`rArr 10k = 2 rArr k = (1)/(5)`.
`therefore "required ratio is" (1)/(5) : 1, i.e., 1:5.`