Question

Find the area of the triangle with vertices $P(4,5)$, $Q(4,-2)$ and $R(-6,2)$.

• A. 21 sq. units
• B. 35 sq. units
• C. 30 sq. units
• D. 40 sq. units

Answer 1

Answer: (B)

Let $\Delta$ be the area of triangle $PQR$. Then,

$\Delta =\frac{1}{2}\left|\begin{array}{ccc}4& 5& 1\\ 4& -2& 1\\ -6& 2& 1\end{array}\right|$

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

$\Delta =\frac{1}{2}\left|\begin{array}{ccc}0& 7& 0\\ 10& -4& 0\\ -6& 2& 1\end{array}\right|$

Expanding along $R_1$, we get

$\Rightarrow \Delta =\frac{1}{2}\left|\left[-7\left(10-0\right)\right]\right|=\frac{1}{2}\left|-70\right|=35$ sq. units