Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, – 2) and B(3, 7).

Let the line segment joining the points A(2, -2) and B(3, 7) is divided by the line 2x+y-4 = 0 into ratio k:1.
Using section formula ((m₁x₂+m₂x₁)/(m₁+m₂), (m₁y₂+m₂y₁)/(m₁+m₂)), the coordinates of point of intersection = ((3k+2)/(7k-2)/(k+1))
Since this point lies on the line 2x+y-4 = 0, so it will satisfy the equar=tion of line. Therefore,
2((3k+2)/(k+1))+((7k-2)/(k+1))-4=0
⇒ (6k+4+7k-2-4k-4)/(k+1) = 0
⇒ 9k-2 = 0 ⇒ k = 2/9
Hence, the line segment joining the points A(2, -2) and B(3, 7) is divided by the line 2x+y-4 = 0 into ratio 2:9.

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