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,

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

Applying $R_1\to R_1-R_2$ and $R_2-R_3$, we get

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

Expanding along $C_3$, we get

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