Sometimes, but only sometimes.
A straight line in two dimensional space will partition it into points on the line, on one side of it and those on the other side of it. The same will apply to some simple curves including simply closed curves. But it will not apply to any curve that crosses itself more than once, nor will it apply to lines in 3-dimensional space.
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It is divided into three regions.
Three points can determine a plane but not 3-d space.
true
Three non-co-linear points are sufficient to uniquely define a single plane.
one