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Area of triangle with vertex (-3,3) (4,4) (5,-3)

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luvgoj | Student, Undergraduate | Honors

Posted July 15, 2013 at 2:48 PM via web

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Area of triangle with vertex (-3,3) (4,4) (5,-3)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 15, 2013 at 3:02 PM (Answer #1)

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The problem provides the vertices of triangle ABC, hence, you may use the following determinant formula to evaluate the area of triangle ABC, such that:

`A_(Delta ABC) = (1/2)|Delta ABC|`

`|Delta ABC| = |[(x_A,y_A,1),(x_B,y_B,1),(x_C,y_C,1)]|`

Replacing the given values of vertices yields:

`|Delta ABC| = |[(-3,3,1),(4,4,1 ),(5,-3,1)]|`

`|Delta ABC| = |-3*4*1 + 4*(-3)*1 + 3*1*5 - 5*4*1 - (-3)*(-3)*1 - 4*3*1|`

`|Delta ABC| = |-12 - 12 + 15 - 20 - 9 - 12|`

`|Delta ABC| = |-50| = 50`

`A_(Delta ABC) = (1/2)*50 = 25`

Hence, evaluating the area of triangle ABC, using determinant formula, yields `A_(Delta ABC) = 25` .

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