Science:Math Exam Resources/Courses/MATH152/April 2016/Question A 02/Hint 1

Given three points $A=(a_{1},a_{2})$, $B=(b_{1},b_{2})$ and $C=(c_{1},c_{2})$ on the plane, the area of triangle $ABC$ is given by

${\frac {1}{2}}\left|\det {\begin{pmatrix}a_{1}&a_{2}&1\\b_{1}&b_{2}&1\\c_{1}&c_{2}&1\end{pmatrix}}\right|.$