Assuming *p*_{0} = (0, 0),
compute the signed area within (0,0), *p*_{1}, *p*_{2}, *p*_{1} + *p*_{2} = (*x*_{1} +
*x*_{2}, *y*_{1} + *y*_{2}).

, the area of
the parallelogram

This is the determinant of the matrix

Note if *p*_{1} = (4,0) and *p*_{2} = (2,4), we are computing the signed area
within (origin, *p*_{1}, *p*_{2}, *p*_{1} + *p*_{2}) which is
= 16 - 0 = 16.

If we compute the signed area is 0 - 16 = -16.