Signed 2D Triangle Area from the Cross Product of Edge Vectors

The signed area of a triangle in the - plane with vertices , , is given by half the component of the cross product of the edge vectors and .

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DETAILS

The edge vectors are
,
.
The cross product of the edge vectors is
.
The signed triangle area is half the component of the cross product:
,
which is equivalent to half the determinant of the matrix formed by the coordinates of when it is embedded in 3D space at :
.
Reference
[1] J. O'Rourke, Computational Geometry in C (Cambridge Tracts in Theoretical Computer Science), 2nd ed., Cambridge: Cambridge University Press, 1998.
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