The line x + y = 3 intersects the pair of straight lines x^2 - 3xy + y^2 = 0 at points A and B. Then the co-ordinates of the mid-point of AB are

Step-by-step solution

Given the equation of the line x + y = 3 y = 3 - x . Substituting y = 3 - x into the equation of the pair of straight lines x^2 - 3xy + y^2 = 0 : x^2 - 3x(3 - x) + (3 - x)^2 = 0 x^2 - 9x + 3x^2 + 9 - 6x + x^2 = 0 5x^2 - 15x + 9 = 0 Let x₁ and x₂ be the roots of this quadratic equation, which represent the x-coordinates of the intersection points A and B. The sum of the roots is x₁ + x₂ = 15 5 = 3 . The x-coordinate of the mid-point of AB is x₁ + x₂ 2 = 3 2 . Since the mid-point lies on the line x + y = 3 , its y-co