Question

Find area of the triangle with vertices at the points in each of the following

(2,7), (1,1), (10,8)

Answer 1

Required area $=\frac{1}{2}\left|\begin{array}{ccc}2& 7& 1\\ 1& 1& 1\\ 10& 8& 1\end{array}\right|=\frac{1}{2}|2(1-8)-7(1-10)+1(8-10)|$
$=\frac{1}{2}|2(-7)-7(-9)+1(-2)|=\frac{1}{2}|-14+63-2|=\frac{47}{2}$sq. unit