Let PQR be a right angled isosceles triangle, right angled at P(2,1) . If the equation of the side Q R is 2 x+y=3 , then the equation of one of the sides other than Q R is

Step-by-step solution

Since P Q R is isosceles right angled triangle. Hence P Q R= P R Q=45^ Let m₁ and m₂ be the slope of line P Q and line P R respectively. Given line Q R is 2 x+y=3 y=-2 x+3 . Hence slope of Q R=m=-2 Since the angle between P Q and R Q is 45^ . Hence aligned & 45^ = m₁-m 1+m₁ m = m₁+2 1-2 m₁ & m₁+2=1-2 m₁ 3 m₁=-1 & m₁=- 1 3 aligned Since P R and P Q are perpendicular lines Hence m₁ m₂=-1 m₂=- 1 m₁ =3 m₂=3 Hence equation of line P Q , aligned & y-1=m₁(x-2)= (- 1 3 )(x-2) & 3 y+x+1=0 aligned Hence equation of line P R