Find the ratio in which the point `P(x,2)` divides the line segment joining the points `A(12,5) and B(4, -3)`. Also find the value of `x`.

Explanation

Let the required ration be k:1.
Then, by section formula, the coordinates of P are `P((4k+12)/(k+1), (-3k +5)/(k+1))`
But, this point is given as P(x, 2).
`therefore (-3k +5)/(k+1) = 2 rArr -3k + 5 = 2k +2 rArr 5k = 3 rArr k = (3)/(5).`
So, the required ratio is 3:5.
Putting `k = (3)/(5)` in P, we get
`x = ({4 xx (3)/(5) + 12})/(((3)/(5) +1)) = (72)/(8) = 9.`
Hence, x = 9.