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,

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

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

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

Expanding along $R_{1}$, we get

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