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A triangle has its three sides equal to ...

A triangle has its three sides equal to `a , b and c` . If the coordinates of its vertices are `A(x_1, y_1),B(x_2,y_2)a n dC(x_3,y_3),` show that `|[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=(a+b+c)(b+c-a)(c+a-b)(a+b-c)`

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$$ \Delta=\frac{1}{2}\left|\begin{array}{lll} x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & y_{3} & 1 \end{array}\right| $$ $$ ...
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