Question

If the area of the triangle formed by $(0,0),(a,0)$ and $(\frac{1}{2},a)$ is equal to $\frac{1}{2}$ sq unit, then the values of $a$ are :

• A. $\pm 2$
• B. $\pm 3$
• C. $\pm 1$
• D. $\pm 4$
• E. $\pm 5$

Answer 1

Answer: (C)

$\pm 1$

$\because$ Area of triangle $=\frac{1}{2}$
$\left|\begin{array}{ccc}0& 0& 1\\ a& 0& 1\\ 1/2& a& 1\end{array}\right|=\frac{1}{2}$
$\therefore \frac{1}{2}=\frac{1}{2}|(a^2-0)|$
$\Rightarrow 1=a^2$
$\Rightarrow 1=a^2$
$\Rightarrow a=\pm 1$