How many of the following statements are true?Four coplanar lines can divide the plane into 6 regions.Five coplanar lines can divide the plane into 8 regions.Six coplanar lines can divide the plane into 7 regions.
Question
How many of the following statements are true?Four coplanar lines can divide the plane into 6 regions.Five coplanar lines can divide the plane into 8 regions.Six coplanar lines can divide the plane into 7 regions.
Solution
To answer this question, we need to understand how many regions coplanar lines can divide a plane into.
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"Four coplanar lines can divide the plane into 6 regions." This statement is true. If you draw four lines on a plane such that no two are parallel and no three intersect at a single point, you will divide the plane into 11 regions.
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"Five coplanar lines can divide the plane into 8 regions." This statement is false. Five lines can divide a plane into a maximum of 16 regions.
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"Six coplanar lines can divide the plane into 7 regions." This statement is false. Six lines can divide a plane into a maximum of 22 regions.
So, only one of the given statements is true.
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