How many possible distinct regions of the plane may be separated by any 3 such lines?
3 distinct lines contained within a plane separate the plane into distinct regions. How many possible distinct regions of the plane may be separated by any 3 such lines?
2 Answers By Expert Tutors
Mathematics Teacher - NCLB Highly Qualified
Take a piece of paper.
Draw three lines from edge to edge with each line intersecting the other two.
Now count the spaces.
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I believe it's 7 because there could be three distinct lines, not all intersecting at one point, so that there's a triangle and 6 other regions formed by extending the triangle's sides indefinitely.
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