In a triangle ABC the coordinate of the vertex A is (1,2) . Equations of the median through B and C are respectively x+y=5 and x=4 . Then the equation of side A B is

Step-by-step solution

Let the vertices be A(1, 2) , B(x₁, y₁) , and C(x₂, y₂) . The median through B is x+y=5 . Since B lies on this line, x₁+y₁=5 . The midpoint of AC lies on this line, so 1+x₂ 2 + 2+y₂ 2 = 5 , which simplifies to x₂+y₂=7 . The median through C is x=4 . Since C lies on this line, x₂=4 . Substituting into x₂+y₂=7 , we get y₂=3 . Thus, C is (4, 3) . The midpoint of AB lies on the median through C ( x=4 ), so 1+x₁ 2 = 4 , which gives x₁=7 . Using x₁+y₁=5 with x₁=7 , we get y₁=-2 . Thus, B is (7, -2) . The equation of side