The area of the triangle with vertices  $(2,7),(1,1),(10,8)$ is

The area of the triangle with the vertices  $(2,7),(1,1),(10,8)$ is

$\Delta =\frac{1}{2}\left|\begin{array}{ccc}2& 7& 1\\ 1& 1& 1\\ 10& 8& 1\end{array}\right|=\frac{1}{2}[-16+63]$

$=\frac{47}{2}$ sq. units.