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Find the area of the triangle with vertices at A(-3,4,0) B(-4,6,-5) C(-1,1,-5)

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blasto63 | Student | (Level 1) Salutatorian

Posted January 26, 2013 at 4:15 PM via web

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Find the area of the triangle with vertices at

A(-3,4,0) B(-4,6,-5) C(-1,1,-5)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted January 26, 2013 at 6:39 PM (Answer #1)

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You need to evaluate the area of triangle using determinant formula such that:

`A = (1/2)|[(x_A,y_A,z_A,1),(x_B,y_B,z_B,1),(x_C,y_C,z_C,1),(1,1,1,1)]|`

Substituting the given coordinates in determinant, yields:

`A = (1/2)|[(-3,4,0,1),(-4,6,-5,1),(-1,1,-5,1),(1,1,1,1)]|`

Evaluating the determinant yields:

`A = (1/2)|56| => A = 28`

Hence, evaluating the area of the given triangle, using determinant formula, yields A = 28.

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