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Answer :

Let the line 2x + y - 4 = 0 divides AB in 1 : k ratio, then the coordinates of the point of division is

\( x \ = \ \frac{2+3k}{k+1} \ and \ y \ = \ \frac{-2+7k}{k+1} \)

The point of intersection lie on both lines

\(\therefore x \ = \ \frac{2+3k}{k+1} \ and \ y \ = \ \frac{-2+7k}{k+1} \) should satisfy 2x + y - 4 = 0

\( \Rightarrow 2( \frac{2+3k}{k+1}) \ + \ (\frac{-2+7k}{k+1}) \ - \ 4 \ = \ 0 \)

\( \Rightarrow 4 \ + \ 6k \ - \ 2 \ + \ 7k \ = \ 4k \ + \ 4 \)

\(\Rightarrow 9k - 2 = 0\)

\( \Rightarrow k \ = \ \frac{2}{9} \)

\( \therefore \) The line 2x + y – 4 = 0 divides the line segment joining the points A(2, –2) and B(3, 7) in ratio 2 : 9 internally.

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