Question

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

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

Answer 1

Answer: (B)

$0$ s unit

Answer 2

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