Answer
$A_{ABC}=21$
Work Step by Step
$A(-4,-4)$
$B(-1, 2)$
$C(2, -6)$
$A_{ABC}=\pm\frac{1}{2}\begin{vmatrix}
-4 & -4 & 1\\
-1 & 2 & 1 \\
2 & -6 & 1
\end{vmatrix}$
$=\pm\frac{1}{2}[-4(2+6)-(-4)(-1-2)+1(6-4)]$
$=\pm\frac{1}{2}(-32-12+2)$
$=\pm\frac{1}{2}.(-42)$
$=\pm21$
Hence $A_{ABC}=21$.
