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 point `P(x,2)` divides AB in the ratio `k:1`.
`therefore" "x=(12xx1+kxx4)/(k+1)and 2=(5xx1+kxx-3)/(k+1)`
Now, `" "2=(5-3k)/(k+1)`
`rArr" "2k+2=-3k+5" "rArr" "5k=3`
`rArr" "k=(3)/(5)`
`therefore` Required ratio = 3: 5
and `" "x=(4k+12)/(k+1)=(4xx(3)/(5)+12)/((3)/(5)+1)=(12+60)/(3+5)=9`
`therefore" "x=9`