If ( | array ccc 2 a & x₁ & y₁ 2 b & x₂ & y₂ 2 c & x₃ & y₃ array |= a b c 2 0 ), then the area of the triangle whose vertices are [ ( x₁ a , y₁ a ), ( x₂ b , y₂ b ), ( x₃ c , y₃ c ) is ]

Step-by-step solution

Given vertices of triangle ( ABC ) are ( A ( x₁ a , y₁ a ), B ( x₂ b , y₂ b ), C ( x₃ c , y₃ c ) ) Now, ( | array ccc 2 a & x₁ & y₁ 2 b & x₂ & y₂ 2 c & x₃ & y₃ array |= a b c 2 (1) ) Taking L.H.S. of the Eq. (1) we have [ | array lll 2 a & x₁ & y₁ 2 h & x₂ & y₂ 2 c & x₃ & y₃ array | ] Now ( R₁ R₁ a , R₂ R₂ a , R₃ R₃ a ) then ( C₁ C₁ 2 ) we have ( | array ccc 2 & x₁ a & y₁ a 2 & x₂ b & y₂ b 2 & x₃ c & y₃ c array | array ccc 1 & x₁ a & y₁ a 1 & x₂ b & y₂ b 1 & x₃ c & y₃ c array ) We know that area od triangle is give