Question

If $(k,2),(2,4)$ and $(3,2)$ are vertices of the triangle of area $4$ square units, then the value of $k$ is/are

• A. $7$
• B. $4$
• C. $-1$
• D. $-2$

Answer 1

Answer: (A), (C)

$-1$

Area of triangle = $4$ square units
$\Rightarrow 4=\frac{1}{2}\left|\begin{array}{ccc}k& 2& 1\\ 2& 4& 1\\ 3& 2& 1\end{array}\right|$
$\Rightarrow 4=\frac{1}{2}\left|k\right(4-2)-2(2-3)+1(4-12\left)\right|$
$\Rightarrow 8=|k\left(2\right)-2(-1)+1(-8)|\Rightarrow 2k-6=\pm 8\Rightarrow 2k=8+6\text{or}2k=-8+6\Rightarrow k=7\text{or}k=-1$