Question

Find the area of the triangle whose vertices are $(-2,6), (3,-6)$ and $(1,5)$.

• A. 30 sq. units
• B. 35 sq. units
• C. 40 sq. units
• D. 15.5 sq. units

Answer 1

Answer: (D)

Let $ \Delta$ be the area of the triangle then,

$\Delta=\frac{1}{2}\left|\begin{matrix}-2&6&1\\ 3&-6&1\\ 1&5&1\end{matrix}\right|$

Applying $R_{1} \rightarrow R_{1} - R_{2}$ and $R_{2} -R_{3}$, we get

$\Delta=\frac{1}{2} \left|\begin{matrix}-5&12&0\\ 2&-11&0\\ 1&5&1\end{matrix}\right|$

Expanding along $C_{3}$, we get

$\Delta=\frac{1}{2}\left|55-24\right|=15.5$ sq. units