Affine invariant for 4 coplanar points ABCD is said to be Area(ACD)/Area(ABC). Can somebody provide the proof of this means why is this invariant under affine transformation?
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The ratio of areas of $ABC$ and $ACD$ is the ratio in which the line $AC$ divides the segment $BD$ (and it is the ratio of the heights of $B$ and $D$ over $AC$ respectively). This later ratio is affine invariant as affine transformations preserve length ratios on any line. Do make sure that your points don't collapse onto a single line though. |
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