Question

The area of the triangle formed by points 1+i, 1 - i , 2i is

• A. $1/2$
• B. $1$
• C. $\sqrt{2}$
• D. $2$

Answer 1

The correct option is B $1$

Now this is a problem of simple geometry , which or lie solved using co- ordinate geometry
$\therefore$ Area of triangle$=\frac{1}{2}[\left|\begin{array}{cc}1& 0\\ 1& 2\end{array}\right|+\left|\begin{array}{cc}0& 1\\ 2& -1\end{array}\right|+\left|\begin{array}{cc}1& 1\\ -1& 1\end{array}\right|]$
$=\frac{1}{2}\left[\right(2-0)+(-2)+(1-(-1)\left)\right]$
$\frac{1}{2}(2-2+2)$
$=1$
Note: Area of polygon with vertices : $(x_1,y_1),(x_2,y_2),----,(x_n,y_n)$
is $A=\frac{1}{2}\{\left|\begin{array}{cc}{x}_1& x_2\\ y_1& y_2\end{array}\right|+\left|\begin{array}{cc}{x}_2& x_3\\ y_2& y_3\end{array}\right|+---+\left|\begin{array}{cc}{x}_n& x_1\\ y_n& y_1\end{array}\right|\}$. points taken in anticlockwise order.