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If I have $2$ vector points and I wish to create a 3rd vector point to make a plane from.

I'd like to make sure the 3rd point I generate doesn't happen to have the same slope.

I can add either $1$ to $y$ or one to $x$ to create it but it might by chance be that this new point is one the line made by point $A$ and $B$ and so therefore not really a plane.

I think I can take the slope of $A \to B$ and normalize it. I should be able to compare that to my slope of $A \to A + X$ which is of course a slope of $X$ and so if the slope of the two lines is equal, I just add the other direction instead.

Does that sound mathematically correct?

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Use the fact that, if $(x, y)$ is a vector, than $(-y, x)$ is orthogonal to it.

So, if your two points are $(a, b)$ and $(c, d)$, then their difference is $(c-a, d-b)$, and $(b-d, c-a)$ is orthogonal to the line between them.

So, let the third point be $(c+b-d, d+c-a)$ (or $(c+r(b-d), d+r(c-a))$ for a real r).