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Blizzard [7]
2 years ago
6

What is the area of triangle ABC?

Mathematics
1 answer:
miskamm [114]2 years ago
8 0

Answer:

<h2>7 square units</h2>

Step-by-step explanation:

As you can observe in the image attached, we know the coordinates of each vertex of the triangle.

To find the area using only its vertex coordinates, we need to use the following formula

A=\frac{1}{2}[x_{1}(y_{2} -y_{3}+x_{2}(y_{3} -y_{1} )+x_{3}(y_{1}-y_{2}  )   )

Where the coordinates are

A(1,1)\\B(4,0)\\C(3,5)

Replacing coordinates, we have

A=\frac{1}{2}[1(0 -5)+4(5 -1 )+3(1-0  )  ]\\A=\frac{1}{2} [-5+16+3]=\frac{1}{2}(14)\\ A=7

Therefore, the area of the triangle is 7 square units. So, the right answer is the second choice.

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<h2>Answer:</h2>

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Step 3: Let's multiply second equation by −35, Next, add the result to the third equation. Therefore:

\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&&+~~\frac{ 1 }{ 5 }~ z&~=~\frac{ 2 }{ 5 }\end{array}

Step 4: solve for z, then for y, then for x:

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x+2(-1)-2=-3 \\ \\ x-2-2=-3 \\ \\ \boxed{x=1}

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