Better Students Ask More Questions.
Given 100 noncollinear points, make a conjecture about the maximum number of lines formed.
2 Answers | add yours
The number of distinct points required to determine a unique line are 2. In the question asked there are 100 non-collinear points. Each of them can determine 99 unique lines with the other points.
But it has to be kept in mind that a line determined by two points A and B is the same even if the position of the points is interchanged, i.e. AB and BA are the same line.
This gives the maximum number of lines that the points can determine as 100*99/2 = 4950
The maximum number of lines that 100 non-collinear points can determine is 4950.
Posted by justaguide on September 11, 2011 at 4:15 AM (Answer #1)
High School Teacher
If no three points out of the 100 are colinear then each pair of points will define a separate line.
So first point will define 99 lines and subsequent points will define one line less till the last point which will not define any new line. Therefore total is 99+98+97+.....+1 which works out to
Sum =n(n+1)/2 = 99*100/2 = 4950
Posted by santaone on September 11, 2011 at 6:45 AM (Answer #2)
Join to answer this question
Join a community of thousands of dedicated teachers and students.