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

1 Answer
Oct 1, 2017

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