Question

The area of the triangle formed by the vertices(-5, 7), (-4, -5) and ( -1, -6) is______

Answer 1

$ar$ (Δ$ABC$)  =   $\frac{1}{2} [ x_{1}(y_{2}-y_{3} ) + x_{2} (y_{3}- y_{1}) + x_{3} (y_{1}-y_{2})$

           = 1/2{-5[-5 -(-6)] + (-4)[-6 - 7] + (-1)[7 - (-5)]}

           = 1/2{-5[-5 + 6] - 4[-13] - 1[7 + 5]}

           = 1/2{-5(1) + 52 - 1(12)}

          = 1/2{-5 + 52 - 12}

           = 1/2(52 - 17)

           = 1/2(35)

           = 17.5 sq. units