Asked • 05/22/19

How to tell whether a point is to the right or left side of a line?

I have a set of points. I want to separate them into 2 distinct sets. To do this, I choose two points (*a* and *b*) and draw an imaginary line between them. Now I want to have all points that are left from this line in one set and those that are right from this line in the other set. How can I tell for any given point *z* whether it is in the left or in the right set? I tried to calculate the angle between *a-z-b* – angles smaller than 180 are on the right hand side, greater than 180 on the left hand side – but because of the definition of ArcCos, the calculated angles are always smaller than 180°. Is there a formula to calculate angles greater than 180° (or any other formula to chose right or left side)?

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