Question

determine the ratio in which the linear equations 2x+y-4=0 divides the line segment joining the points A(2,-2) and B(3,7)

Answer 1

Hey

Let point of intersection be ( x , y ) satisfying the eqn. ----> ( i )

And assume the ratio is k : 1 ----> ( ii )

Then, x ≡ ( 3k + 2 ) / ( k + 1 )  --> ( iii )
Also, y ≡  ( 7k - 2 ) / ( k + 1 )   --> ( iv )

Putting the values of 'x' and 'y' from ( iii ), ( iv ) in Eqn.
---> 2 ( 3k + 2 ) + ( 7k - 2 ) - 4 ( k + 1 ) = 0
==> 6k + 4 + 7k - 2 - 4k - 4 = 0
==> 9k = 2
==> k = 2/9

Hence, The desired ratio is 2 : 9 √√