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Question
Find the area of the triangle with vertice at the point:
(−1, −8), (−2, −3) and (3, 2)
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Solution
\[∆ = \frac{1}{2}\begin{vmatrix}- 1 & - 8 & 1 \\ - 2 & - 3 & 1 \\ 3 & 2 & 1\end{vmatrix} \]
\[ ∆ = \frac{1}{2}\begin{vmatrix}- 1 & - 8 & 1 \\ - 1 & 5 & 0 \\ 3 & 2 & 1\end{vmatrix} \left[\text{ Applying }R_2 \to R_2 - R_1 \right]\]
\[ ∆ = \frac{1}{2}\begin{vmatrix}- 1 & - 8 & 1 \\ - 1 & 5 & 0 \\ 4 & 10 & 0\end{vmatrix} \left[\text{ Applying }R_3 \to R_3 - R_1 \right]\]
\[ ∆ = \frac{1}{2}\begin{vmatrix}- 1 & 5 \\ 4 & 10\end{vmatrix}\]
\[ ∆ = \frac{1}{2}\left| - 10 - 20 \right|\]
\[ ∆ = \frac{1}{2}\left( 30 \right) = 15\text{ square units }\]
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