The document considers 5 non-collinear points (A, B, C, D, E) and calculates the number of lines that can be drawn between two points. It determines that there are 4 lines through point A, 3 additional lines through point B, 2 more lines through point C, and 1 final line through point D/E, for a total of 4 + 3 + 2 + 1 = 10 lines.

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
DE

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
DE
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
DE
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
DE
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
DE
There is 1 additional
line 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
DE
4 + 3 + 2 + 1 = 10
10 lines