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If the area of the triangle with vertices $(x, 0)$, $(1,1)$ and $(0,2)$ is $4$ sq units, then the value of $x$ is
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Verified Answer
The correct answer is:
$-6$
We have,
$\frac{1}{2}\left|\begin{array}{lll}x & 0 & 1 \\ 1 & 1 & 1 \\ 0 & 2 & 1\end{array}\right|=\pm 4$
$\Rightarrow \quad x(1-2)+1(2-0)=\pm 8$
$\Rightarrow \quad-x+2=\pm 8$
$\Rightarrow \quad \forall=2 \pm 8 \Rightarrow x=10,-6$
$\frac{1}{2}\left|\begin{array}{lll}x & 0 & 1 \\ 1 & 1 & 1 \\ 0 & 2 & 1\end{array}\right|=\pm 4$
$\Rightarrow \quad x(1-2)+1(2-0)=\pm 8$
$\Rightarrow \quad-x+2=\pm 8$
$\Rightarrow \quad \forall=2 \pm 8 \Rightarrow x=10,-6$
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