Proof the area of a given triangle with coordinates is half determinant – math.stackexchange.com

Proof the area of a given triangle with coordinates is half determinant – math.stackexchange.com

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I was given a problem, tried to solved it but couldn't get to a solution. It goes like that: There's a triangle ABC with area S. $$ \vec{AB} = (a,b) $$ $$ \vec{AC} = (c,d) $$ Prove that $$ S = ...

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