Question

Find the values of $K$ if Area of the triangle is $4$ sq. units and vertices are $\left(k0\right)$ $\left(40\right)$ $\left(02\right)$ using determinants.

Answer 1

$\frac{1}{2}\left|\begin{array}{ccc}K& 0& 1\\ 4& 0& 1\\ 0& 2& 1\end{array}\right|=\pm 4$
$K=(0-2)-0\left(0\right)+1\left(8\right)=\pm 8$
$-2K+8=\pm 8$
$-2K=8-8$

$-2K=0$
$K=0$
or $-2K=-8-8$
$2K=16$
$K=8$