Question

Find the area of the triangle with vertices $ (2,3), $ $ (0,\,\,1) $ and $ (1,\,\,2) $ .

• A. $\frac {1}{2} $ sq. unit
• B. $ 0 $ sq. unit
• C. $ 2 $ sq. units
• D. $ 2\frac {1}{2} $ sq. units

Answer 1

Answer: (B)

Given vertices of triangle are $ (2,\,\,3),(0,\,\,1) $ and $ (1,\,2) $
$ \therefore $ Area of triangle
$=\frac{1}{2}\left| \begin{matrix} 2 & 3 & 1 \\ 0 & 1 & 1 \\ 1 & 2 & 1 \\ \end{matrix} \right| $
$=\frac{1}{2}[2(1-2(-3(-1)+1(0-1)] $
$=\frac{1}{2}[2(-1)+3-1] $
$=\frac{1}{2}[-2+3-1]=0 $