Question

Find the area of a triangle whose vertices are $A(3,4),B(-1,2),$ and $C(2,3)$.

Answer 1

Area of triangle with vertices $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$ is given by $A$:

$A=\frac{1}{2}\left|\begin{array}{cc}(x_1-x_2)& (x_2-x_3)\\ (y_1-y_2)& (y_2-y_3)\end{array}\right|$

$=\frac{1}{2}\left|\begin{array}{cc}(3+1)& (-1-2)\\ (4-2)& (2-3)\end{array}\right|$

$=\frac{1}{2}[-4-(-6\left)\right]$

$\Rightarrow A=1$