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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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Earn +20 ptsQ: Does a line separate space into three distinct sets of points?
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When you Visualize 2 distinct points on a line. The points divide the line into separate regions. How many distinct regions is the line divided into?
It is divided into three regions.
Can three points determine space?
Three points can determine a plane but not 3-d space.
Any three points lie on a distinct line?
true
If three distinct points are not col-linear how many planes can possibly contain the three points?
Three non-co-linear points are sufficient to uniquely define a single plane.
How many planes are determined by three distinct points that are not on the same line?
one
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