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Question 33
Ten straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions (including finite and infinite regions) into which the plane would be divided by the lines is
Solution
If there are 'm' non-parallel lines, then theĀ maximumĀ numberĀ of regions into which the plane is divided isĀ given by
[m(m+1)/2]+1
In this case, 'm' = 10
So, the number of regions into which the plane is divided is (10*11/2) + 1 = 56
Ā
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