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)
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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 √√
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 √√
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