The equal sides of an isosceles triangle are given by equations 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

Let ABC be the isosceles triangle where AB = AC Hence Bisector of Angle B A C will also be the perpendicular on line BC . Let m₁ and m be the slopes of bisector lines AP and line B C respectively. Equation of Bisector lines (AP) are aligned & 7 x-y+3 49+1 = (x+y-3) (1)+(1) & x-3 y+6=0 and 3 x+y-12=0 aligned Here m₁= 1 3 Since AP BC m₁ m=-1 m=-3 Here m₁=-3 Since AP BC m₁ m=-1 m= ( 1 3 ) Since m is integer (given) Hence m=-3