Question

Using determinant, find the area of the triangle whose vertices are :
$(-3,5),(3,-6)$ and $(7,2).$

Answer 1

We know that area is given by

$\frac{1}{2}\Vert \begin{array}{ccc}-3& 5& 1\\ 3& -6& 1\\ 7& 2& 1\end{array}\Vert$modulus

$=\frac{1}{2}(-3(-6-2)-5(3-7)+1(6+42\left)\right)$

$=\frac{1}{2}(24+20+48)$]

$=\frac{92}{2}=46$