Chapter 6.3, Problem 4E

Consider the area A of the triangle with vertices $\left[\begin{array}{l}{a}_1\\ a_2\end{array}\right]$ , $\left[\begin{array}{l}{b}_1\\ b_2\end{array}\right],\left[\begin{array}{l}{c}_1\\ c_2\end{array}\right]$ . Express A in terms of $\det \left[\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ 1& 1& 1\end{array}\right]$ .