The straight line x+y+1=0 bisects an angle between a pair of lines, of which one is 2 x-3 y+4=0 . Then the equation of the other line in that pair is

Step-by-step solution

Point of intersection of lines x+y+1=0 and 2 x-3 y+4=0 is A (- 7 5 , 2 5 ) . Now, Let a point P(-2,0) on the line 2 x-3 y+4=0 and the image of point P(-2,0) w.r.t. line x+y+1=0 lying on the other line in the bisector pair. If the coordinate of image of point P(-2,0) w.r.t. line x+y+1=0 is (h, k) , then array ll h+2 1 = k-0 1 =-2 -2+1 2 =1 h=-1 and k=1 & (h, k)=(-1,1) array Now, equation of required bisector of angle is line joining the points A (- 7 5 , 2 5 ) and (-1,1) is gathered y-1= 3 5 2 5 (x+1) 2 y-2=3 x+3 3