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

1. (1,4)
2. (7,-2)
3. (4,1)
4. (-2,7)

Hello student,
The equation of median through B is x+y = 5. The point B lies on it so the coordinates of B are (x₁, 5-x₁)
Now CF is a median through C, so coordiantes of F i.e. mid-point of AB are
((x₁+1)/2, (5 – x₁+ 2)/2)
Now this lies on x = 4 so this means (x₁+1)/2 = 4
This gives x₁ = 7
Hence, the cooridnates of B are (7, -2).