Determinants / find area of a triangle using the determinant method. In the picture below why is the area equal to 0

Question

Why is the area of triangle equal to 0

Answer 1

Best for you to try and draw a picture of this:

$P$ is a point on the line segment $AB$. Meaning that the "triangle" $ABP$, having perimeter line segments $AB$, $BP$ and $PA$, is just the line segment $AB$ itself (since all 3 of the perimeter line segments are subsets of $AB$).

Now we can say that the area of $ABP$ equals the area of $AB$, which is $0$ because the area of a line segment is $0$ (line segments have effectively $0$ width, so $area=length\times 0=0$)