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

Area of triangle $=\frac{1}{2}\left|\left|\begin{array}{ccc}x& 0& 1\\ 1& 1& 1\\ 0& 2& 1\end{array}\right|\right|=4$

$\Rightarrow |x(1-2)-1(0-2)+0|=8$

$\Rightarrow |-x+2|=|x-2|=8$

$\Rightarrow x-2=\pm 8\Rightarrow x=\pm 8+2=-6,10$