Question

If the area of triangle formed by the points $(\alpha, 0), (0, 1)$ and $(-1, 0)$ is 20 s units, then $\alpha$ is

• A. 20
• B. 19
• C. 39
• D. -19

Answer 1

Answer: (C)

39

Answer 2

$\Delta = \frac{1}{2}\begin{vmatrix}\alpha&0&1\\\ 0&1&1\\\ -1&0&1\end{vmatrix} = \pm20$
Expanding along $R_1$, we get
$20 = \frac{1}{2} \left(\alpha\left(1\right) + 1\left(1\right)\right)$
$\Rightarrow 20 =\frac{1}{2}\left(\alpha+1\right)$
$\Rightarrow \alpha +1 =40 \Rightarrow \alpha =39$