Size of a triangle using determinant

Question

find the size of a triangle using (determinant) with the following points:
$(x_1,y_1)=(1,-2)$
$(x_2,y_2)=(-4,-2)$
$(x_3,y_3)=(-5,-1)$

How should I place those points in the determinant? or firstly in a matrix?

Answer 1

The determinant of two vectors is the area of the parallelogram spanned by them.

If you could arrange the above triangle to be at the origin, then the determinant of the two vectors centered at the origin would be twice the area of the triangle.

Answer 2

I woulad say:

$A=\frac{1}{2}abs\left(\begin{vmatrix} x_{1} & y_{1}& 1\\ x_{2} & y_{2}& 1\\ x_{3} & y_{3}& 1 \end{vmatrix}\right)$