Table of Contents
- 1 What is the maximum number of straight lines that can be drawn with any four points in a plane such that each line contains at least two of these points?
- 2 How many lines can be drawn through a plane?
- 3 What is the maximum number of points of intersection on a plane?
- 4 What is the maximum number of regions a plane can divide?
What is the maximum number of straight lines that can be drawn with any four points in a plane such that each line contains at least two of these points?
6
= 3.4 2 ! 2 ! Hence, the maximum number of straight lines that can be drawn with any four points in a plane such that each line contains at least two of these points is 6.
How many lines can be drawn through a plane?
Thus, through any two points in a plane, exactly one line can be drawn.
How many lines can be drawn on a plane?
The answer is always 3. According to the question, the answer boils down to finding the mid point of the altitudes and the perpendicular line passing through it.
What is the maximum points of intersection of 10 distinct lines?
If follows, then, that the maximum number of points of intersection when 10 lines are drawn in a plane would be the 8th term in the sequence, or 45 points.
What is the maximum number of points of intersection on a plane?
3. The maximum number of points of intersection when 3 lines are drawn in a plane, as shown, is 3 points. 4. The maximum number of points of intersection when 4 lines are drawn in a plane, as shown, is 6 points. 5. The maximum number of points of intersection when 5 lines are drawn in a plane, as shown, is 10 points.
What is the maximum number of regions a plane can divide?
One line can divide a plane into two regions, two non-parallel lines can divide a plane into 4 regions and three non-parallel lines can divide into 7 regions, and so on. When the n th line is added to a cluster of (n-1) lines then the maximum number of extra regions formed is equal to n.
How many regions can a line cross over a line?
Leaving that point on one side of the third line means that the line won’t be able to cross all four already existent regions, but at most only three – one more than there are lines. This gives a clue to a general case.
How many regions can be formed from a cluster of lines?
One line can divide a plane into two regions, two non-parallel lines can divide a plane into 4 regions and three non-parallel lines can divide into 7 regions and so on. When the n th line is added to a cluster of (n-1) lines then the maximum number of extra regions formed is equal to n. Now solve the recursion as follows: