Question

Se A(0 , 0), B(2 , y), C(- 4 , 2y) e a área do triangulo ABC é igual a 8, então o valor de y é?​

Answer 1

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$\tt{\partial}=\begin{vmatrix}\sf{0}&\sf{0}&\sf{1}\\\sf{2}&\sf{y}&\sf{1}\\\sf{-4}&\sf{2y}&\sf{1}\end{vmatrix}$

$\sf{det~\partial=1\cdot(4y+4y)=8y}\\\sf{A=\dfrac{1}{2}|det~\partial|}\\\sf{\diagup\!\!\!8=\dfrac{\diagup\!\!\!8y}{2}}\\\sf{1=\dfrac{y}{2}}\\\sf{y=2\cdot1}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{y=2\checkmark}}}}}$