Find the ratio in which the line segment joining the points`(3,\ 10)\ a n d\ (6,\ 8)\ i s\ d i v i d e d\ b y\ (1,\ 6)`.

Explanation

Let the point `A(-1, 6)` divide the line joining `B(-3, 10)` and `C(6, -8)` in the ratio k:1. Then, the co-ordinates of A are `((6k-3)/(k+1), (-8k+10)/(k+1))*[because "internally ratio "((m_(1)x_(2)+m_(2)x_(1))/(m_(1)+m_(2)), (m_(1)y_(2)+m_(2)y_(1))/(m_(1)+m_(2)))]`
But, the co-ordinates of A are given by (-1, 6).
`therefore" "(6k-3)/(k+1)=-1" "and " "(-8k+10)/(k+1)=6`

`rArr" "6k-3=-k-1" "and " "-8k+10=6k+6`
`rArr " "6k+k=-1+3" "and " "-8k-6k=6-10`
`rArr" "7k=2 " "and " "-14k=-4" "rArr" "k=(2)/(7)`
So, the point A divides BC in the ratio 2 : 7.