Q84 / 180 · COMEDK 2013 · Mathematics

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

  • A
    $-2$
  • B
    $-4$
  • Correct answer
    C
    $-6$
  • D
    $8$

Solution

We have, $\frac{1}{2}\left|\begin{array}{lll}x & 0 & 1 \\ 1 & 1 & 1 \\ 0 & 2 & 1\end{array}\right|=\pm 4$ $\Rightarrow \quad x(1-2)+1(2-0)=\pm 8$ $\Rightarrow \quad-x+2=\pm 8$ $\Rightarrow \quad \forall=2 \pm 8 \Rightarrow x=10,-6$

Hence, the correct answer is option: 'C'.

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