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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

Relevance
  • ?
    Lv 5
    1 decade ago
    Favorite 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.

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