Question

Area of the triangle with vertices $(-2,2),(1,5)$and $(6,-1)$ is

• A. 15
• B. 3/5
• C. 29/2
• D. 33/2
• E. 35/2

Answer 1

Answer: (D)

Area of triangle having vertices $\left(x_1,y_1\right),\left(x_2,y_2\right)$ and $\left(x_3,y_3\right)$ is given by
Area $=\frac{1}{2}\left|\begin{array}{ccc}{x}_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right|$
$\therefore$ Required area $=\frac{1}{2}\left|\begin{array}{ccc}-2& 2& 1\\ 1& 5& 1\\ 6& -1& 1\end{array}\right|$
$=\frac{1}{2}[-2(5+1)-2(1-6)+1(-1-30)]$
$=\frac{1}{2}[-12+10-31]$
$=\frac{-33}{2}$
$\therefore$ Area $=\frac{33}{2}$ sq units