id: 06520643
dt: j
an: 2016a.00645
au: Palmer, Katrina
ti: Geometric view connecting determinants and area.
so: Consortium 108, 1-2 (2015).
py: 2015
pu: COMAP (Consortium for Mathematics and Its Applications), Bedford, MA
la: EN
cc: G70 U70 E50
ut: analytic geometry; Cartesian geometry; coordinate geometry; parallelograms;
area; visualization; geometric proofs; geometry software; determinants;
linear algebra; vectors; rectangles; trapezoids
ci:
li:
ab: Summary: I love finding new and interesting proofs and demonstrations of
geometric theorems particularly ones that are visual. One of my
favorite theorems in coordinate geometry states that the area of the
parallelogram $ABCD$ with vertices at $A(0,0)$, $B(a,b)$, $C(a+c,b+d)$
and $D(c,d)$ is equal to the product $ad-bc$. This editionâ€™s Column
gives a nice visual demonstration, using Geometerâ€™s SketchPad, of
this theorem when applied to any parallelogram, not just one with a
vertex at the origin.
rv: