Question

If the area of the triangle with vertices $(x,0),(1,1)$ and $(0,2)$ is $4$ square units, then the value of $x$ is:

• A. $-2$
• B. $-4$
• C. $-6$
• D. $8$

Answer 1

The correct option is C

$-6$

Explanation for the correct option.

Given that coordinates of triangle, $(x,0),(1,1)$ and $(0,2)$.

Area of triangle $=\frac{1}{2}\left|\right|\begin{array}{lll}x& 0& 1\\ 1& 1& 1\\ 0& 2& 1\end{array}\left|\right|$
$\begin{array}{rcl}\frac{1}{2}\left|\right|\begin{array}{lll}x& 0& 1\\ 1& 1& 1\\ 0& 2& 1\end{array}\left|\right|& =& 4\\ x-2& =& \pm 8\\ x& =& \pm 8+2\\ x& =& -6,10\end{array}$

Hence, option C is correct.