In a A B C , if coordinates of point A is (1,2) and equation of the medians through B and C are x+y=5 and x=4 respectively, then the coordinates of B is

Step-by-step solution

Let the coordinates of A be (1,2) . Let the median through B be L₁: x+y=5 and the median through C be L₂: x=4 . The centroid G is the intersection of the medians L₁ and L₂ . Solving x+y=5 and x=4 , we get 4+y=5 , so y=1 . Thus, G = (4,1) . Let B = (x_B, y_B) . Since B lies on the median x+y=5 , we have x_B + y_B = 5 , or y_B = 5 - x_B . Thus, B = (x_B, 5-x_B) . Let M_C be the midpoint of AB . Since M_C lies on the median x=4 , the x-coordinate of M_C is 4 . The midpoint M_C is given by ( x_B+1 2 , y_B+2 2 ) . Equat