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 given line divides the line segment joining the points A(2,-2)≡(x1,y1) and B(3,7)≡(x2,y2) in ratio m1:m2 = k:1
∴ x = (m1x2 + m2x1)/(m1+m2) ⇒ x = (k × 3 + 1 × 2)/(k+1) = (3k+2)/(k+1)
And y = (m1y2 + m2y1)/(m1+m2) = (k × 7 + 1 × -2)/(k+1) = (7k-2)/(k+1)
This point also lies on 2x+y-4=0
Put the value of x and y in the given equation
∴ 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
∴ The required ratio is 2:9.