Determine the ratio in which the …

Excuse me the ratio is given or not we assuming the ratio or given ratio

in the ratio m₁: m₂ is given by the Section Formula. P (x, y) = [(mx₂ + nx₁) / (m + n) , (my₂ + ny₁) / (m + n)] Let the given line 2x + y - 4 = 0 divide the line segment joining the points A(2, - 2) and B(3, 7) in a ratio k: 1 at point C. Coordinates of the point of divison C (x, y) = [(3k + 2) / (k + 1), (7k - 2) / (k + 1)] Hence, x = (3k + 2) / (k + 1), y = (7k - 2) / (k + 1) This point C also lies on 2x + y - 4 = 0 .....(1) By substituting the values of C(x, y) in Equation(1), 2[(3k + 2) / (k + 1)] + [(7k - 2) / (k + 1)] - 4 = 0 [6k + 4 + 7k - 2 - 4k - 4] / (k + 1) = 0 (By Cross multiplying & Transposing) 9k - 2 = 0 k = 2/9 Therefore, the ratio in which the line 2x + y - 4 = 0 divides the line segment joining the points A (2, 2) and B (3, 7) is 2:9 internally.