Two equal sides of an isosceles triangle are given by (7 x-y+3=0 ) and (x+y-3=0 ). If the slope (m ) of the third side is an integer, then (m= )

Step-by-step solution

Given equation of sides are ( array l 7 x-y+3=0 (i) x+y-3=0 (ii) array ) Equation of angle bisectors of Eqs. (i) and (ii) are ( aligned & 7 x-y+3 49+1 = x+y-3 1+1 & 7 x-y+3 50 = x+y-3 2 & 7 x-y+3 5 = x+y-3 1 & 7 x-y+3 5 =(x+y-3) & or 7 x-y+3 5 =-(x+y-3) & 7 x-y+3=5 x+5 y-15 & or 7 x-y+3=-5 x-5 y+15 & 2 x-6 y+12=0 & or 12 x+4 y-12=0 & x-3 y+6=0 or 3 x+y-3=0 & Slope = 1 3 , Slope =-3 (integer) aligned ) Here, third side is parallel to one angle bisector. ( ) Required slope of third side is -3 .