1. 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).

Consider line 2x + y – 4 = 0 divides line AB joined by the two points A(2, -2) and B(3, 7) in k : 1 ratio. Coordinates of point of division can be given as follows: x = (2 + 3k)/(k + 1) and y = (-2 + 7k)/(k + 1) Substituting the values of x and y given equation, i.e. 2x + y – 4 = 0, we have 2{(2 + 3k)/(k + 1)} + {(-2 + 7k)/(k + 1)} – 4 = 0 (4 + 6k)/(k + 1) + (-2 + 7k)/(k + 1) = 4 4 + 6k – 2 + 7k = 4(k+1) -2 + 9k = 0 Or k = 2/9 Hence, the ratio is 2: 9.