Question

The equation of the line which passes through the intersection of the lines x + 2y + 3 = 0 and 3x + 4y + 7 = 0 and is perpendicular the line x – y = 8 is

(A)  x + 2y + 3 = 0

(B)  x + y - 2 = 0

(C)   x + y + 2 = 0

(D)  3x + 3y - 4 = 0 

Answer 1

Correct option  (C)  x +  y + 2 = 0 

Explanation :

Direct Method: Intersection of the lines x + 2y + 3 = 0 and 3x + 4y + 7 = 0 is ( 1, 1). Slope of the line x – y + 8 = 0 is 1. Hence, the equation of the required line is

 y + 1 = -1(x + 1) or  x + y + 2 = 0