Answer
$A_{ABC}=9$
Work Step by Step
$A(5,-4)$
$B(6, 3)$
$C(8, -1)$
$A_{ABC}=\pm\frac{1}{2}\begin{vmatrix}
5 & -4 & 1\\
6 & 3 & 1 \\
8 & -1 & 1
\end{vmatrix}$
$=\pm\frac{1}{2}[5(3+1)-(-4)(6-8)+1(-6-24)]$
$=\pm\frac{1}{2}(20-8-30)$
$=\pm\frac{1}{2}.(-18)$
$=\pm9$
Hence $A_{ABC}=9$.
