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What is m if area of triangle ABC is 23?A(2,-3),B(3,5),C(-3,m)

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lightjazz | Student, Undergraduate | eNoter

Posted August 22, 2012 at 11:07 AM via web

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What is m if area of triangle ABC is 23?

A(2,-3),B(3,5),C(-3,m)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted August 22, 2012 at 11:21 AM (Answer #1)

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Since the problem provides the coordinates of the vertices, hence, you should evaluate the area of triangle using the following formula:

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

`A = (1/2)*|[[2,-3,1],[3,5,1],[-3,m,1]]|`

`A = (1/2)|10 + 3m + 9 + 15 - 2m + 9| `

Since the problem provides the value of area, hence you need to substitute 23 for A such that:

`23 = (1/2)*|43 + m| => 46 = 43 + m => m = 46 - 43 => m = 3`

Hence, evaluating the value of y coordinate m, under the given conditions, yields m = 3.

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