Example Lines through Noncollinear Points

MATH 302 - Module 1 - Lines, Parts of Lines and First Principles

1. Example: Lines through Non-collinear Points Consider points A , B , C , D , and E no three of which are collinear. How many lines can be drawn through these points such that each line contains two of the points? A   B   C   D   E  

2. Example: Lines through Non-collinear Points Consider points A , B , C , D , and E no three of which are collinear. How many lines can be drawn through these points such that each line contains two of the points? A   B   C   D   E   There are 4 lines through point A and one other point 4

3. Example: Lines through Non-collinear Points Consider points A , B , C , D , and E no three of which are collinear. How many lines can be drawn through these points such that each line contains two of the points? A   B   C   D   E   There are 3 additional lines through point B and one additional point 4 + 3

4. Example: Lines through Non-collinear Points Consider points A , B , C , D , and E no three of which are collinear. How many lines can be drawn through these points such that each line contains two of the points? A   B   C   D   E   There are 2 additional lines through point C and one additional point 4 + 3 + 2

5. Example: Lines through Non-collinear Points Consider points A , B , C , D , and E no three of which are collinear. How many lines can be drawn through these points such that each line contains two of the points? A   B   C   D   E   There is 1 additional lines through point C and one additional point 4 + 3 + 2 + 1

6. Example: Lines through Non-collinear Points Consider points A , B , C , D , and E no three of which are collinear. How many lines can be drawn through these points such that each line contains two of the points? A   B   C   D   E   4 + 3 + 2 + 1 = 10 10 lines