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#