In ABC the coordinates of the vertex A are (-3,1) . If the equation of the median through B is 2 x+y-3=0 and the equation of the bisector of angle C is 7 x -4 y -1=0 , then the equation of the side BC is

Step-by-step solution

M= Mid point of A C= ( -3+h 2 , 1+k 2 ) (h, k) lies on 7 x-4 y-1=0 . 7 h-4 k-1=0 h= 4 k+1 7 M= ( -3+ 4 k+1 7 2 , 1+k 2 )= (-10+2 k, 1+k 2 ) M lies on B M . 2(-10+2 k)+ ( 1+k 2 )-3=0 k=5 from equation (2) h= 4 5+1 7 =3 (h, k)=(3,5) Slope of line A C=m₁= 5-1 3+3 = 4 6 = 2 3 Slope of line CN =m₂= 7 4 . Let slope of B C is m . Since B C N= N C A . | m- 7 4 1+ 7 4 m |= | 7 4 - 2 3 1+ 7 4 2 3 |= 1 2 m- 7 4 1+ 7 4 m = 1 2 m=18 Equation of B C is aligned & (y-5)=m(x-3) (y-5)=18(x-3) & 18 x-y=49 . aligned