Question

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

(2, 7), (1, 1) and (10, 8)

Answer 1

\[∆ = \frac{1}{2}\begin{vmatrix}2 & 7 & 1 \\ 1 & 1 & 1 \\ 10 & 8 & 1\end{vmatrix} \] 

\[ ∆ = \frac{1}{2}\begin{vmatrix}2 & 7 & 1 \\ - 1 & - 6 & 0 \\ 10 & 8 & 1\end{vmatrix} \left[\text{ Applying }R_2 \to R_2 - R_1 \right]\] 

\[ ∆ = \frac{1}{2}\begin{vmatrix}2 & 7 & 1 \\ - 1 & - 6 & 0 \\ 8 & 1 & 0\end{vmatrix} \left[\text{ Applying }R_3 \to R_3 - R_1 \right]\] 

\[ ∆ = \frac{1}{2}\begin{vmatrix}- 1 & - 6 \\ 8 & 1\end{vmatrix}\] 

\[ ∆ = \frac{1}{2}\left( - 1 + 48 \right)\] 

\[ ∆ = \frac{1}{2}\left( 47 \right) = \frac{47}{2}\text{ square units }\]