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Question: What is the greatest number of regions into which three straight lines (of infinite extent) can divide the plane?

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Question:
What is the greatest number of regions into which three straight lines (of infinite extent) can divide the plane?

Options:
(1) 5
(2) 6
(3) 7
(4) 8

1 Answer

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by (19.9k points)

Step-by-Step Explanation:

General Formula for Maximum Regions Divided by Lines:
The maximum number of regions R that n straight lines can divide the plane into is given by:

 image 

where n is the number of lines.

image

  1. Visualizing the Configuration: To achieve the maximum number of regions:

    • The lines must intersect in such a way that no two lines are parallel.

    • No three lines should intersect at the same point.

    • This creates 7 regions in total.

Final Answer:

(3) 7

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