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Given the points A(-3,-1),B(1,5),C(2,y), calculate y if area of triangle ABC is 5 ?

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yapayapa | Honors

Posted August 30, 2013 at 8:34 AM via web

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Given the points A(-3,-1),B(1,5),C(2,y), calculate y if area of triangle ABC is 5 ?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted August 30, 2013 at 9:06 AM (Answer #1)

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Since the problem provides the vertices of triangle `ABC, ` you need to use the following determinant formula to evaluate the area of triangle `ABC` , such that:

`A = (1/2)*|Delta|`

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

`Delta = [(-3,-1,1),(1,5,1),(2,y,1)]`

`Delta = -15 + y - 2 - 10 + 3y + 1 => Delta = 4y - 26`

The problem provides the information that the area of triangle `ABC` is of 5, such that:

`5 = (1/2)*|4y - 26| => 10 = 4y - 26 => 4y = 36 => y = 9`

Hence, evaluating the requested coordinate y, under the given conditions, yields `y = 9` .

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