Example: Lines through Non-collinear PointsConsider 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

 

Example: Lines through Non-collinear PointsConsider 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

Example: Lines through Non-collinear PointsConsider 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

Example: Lines through Non-collinear PointsConsider 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

Example: Lines through Non-collinear PointsConsider 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 line through point C and one additional

point

4 + 3 + 2 + 1

Example: Lines through Non-collinear PointsConsider 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