In a Δ A B C , 2 x + 3 y + 1 = 0 , x + 2 y - 2 = 0 are the perpendicular bisectors of its sides A B and A C respectively and if A = ( 3 , 2 ) , then the equation of the side B C is

Step-by-step solution

The figure below represents the triangle and lines bisectors of its sides. The equation of A B is   3 x - 2 y + c = 0 . As it passes through   A ( 3 , 2 ) , the value of c = - 5 . Thus, 3 x - 2 y - 5 = 0 . The coordinates of D is ( 1 , - 1 ) as D is the mid-point of A B . Consider the coordinates of B are ( α , β ) . 3 + α 2 = 1 ,   2 + β 2 = - 1 α = - 1 ,   β = - 4 B ( - 1 , - 4 ) Similarly, the equation of A C is 2 x - y + c = 0 . As it passes through ( 3 , 2 ) ,