Question

Determine the ratio in which the line 2x+y=4 divide the line joining the points (2,-2) and (3,1) ?

Answer 1

The ratio is `2:3`

Explanation:

Let `P(x,y)` be the point of intersection of the line `2x+y=4` and the line joining `A(2,-2) and B(3,1)`,
Assume that `P` divides line segment `AB` in the ration of `1:n`,
By section formula,
`P(x,y)= ((1xx3+nxx2)/(1+n), (1xx1+n(-2))/(1+n))`
`=((3+2n)/(1+n), (1-2n)/(1+n))`
Substituting `P(x,y)` in `2x+y-4=0`,
`(2*(3+2n))/(1+n)+(1-2n)/(1+n)-4=0`
`=> (6+4n)/(1+n)+(1-2n)/(1+n)=4`
`=> 7+2n=4+4n`
`=> 2n=7-4`
`=> n=3/2`

Hence, the ratio is `2:3`