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Three distinct lines, all contained in a plane, separate the plane into distinct regions.?
What are all of the possible numbers of distinct regions of the plane that may be separated by any 3 such lines?
(Note: Do not include any of the points on the 3 lines in your count of distinct regions.)
A. 3, 4, 7
B. 3, 6, 7
C. 4, 5, 6
D. 4, 5, 7
E. 4, 6, 7
1 Answer
- ?Lv 51 decade agoFavorite Answer
Cases:
If all three of them are parallel: we have 4 regions
If two of them are parallel and one is not: 6 regions
If no two lines are parallel: 7 regions
=> E.
Explanation: draw each case alone and count the regions.