Question

Find the area of the triangle with vertice at the point:

 (−1, −8), (−2, −3) and (3, 2)

Answer 1

\[∆ = \frac{1}{2}\begin{vmatrix}- 1 & - 8 & 1 \\ - 2 & - 3 & 1 \\ 3 & 2 & 1\end{vmatrix} \] 

\[ ∆ = \frac{1}{2}\begin{vmatrix}- 1 & - 8 & 1 \\ - 1 & 5 & 0 \\ 3 & 2 & 1\end{vmatrix} \left[\text{ Applying }R_2 \to R_2 - R_1 \right]\] 

\[ ∆ = \frac{1}{2}\begin{vmatrix}- 1 & - 8 & 1 \\ - 1 & 5 & 0 \\ 4 & 10 & 0\end{vmatrix} \left[\text{ Applying }R_3 \to R_3 - R_1 \right]\] 

\[ ∆ = \frac{1}{2}\begin{vmatrix}- 1 & 5 \\ 4 & 10\end{vmatrix}\] 

\[ ∆ = \frac{1}{2}\left| - 10 - 20 \right|\] 

\[ ∆ = \frac{1}{2}\left( 30 \right) = 15\text{ square units }\]