The six points A, B, C, D, E, and F are located on a circle, as shown below. How many line segments having two of these points as endpoints can be drawn?

Question

The six points A, B, C, D, E, and F are located on a circle, as shown below. How many line segments having two of these points as endpoints can be drawn?

Answer 1

 

A to B segment AB

A to C segment AC

A to D segment AD

A to E segment AE

A to F segment AF

B to C              BC (B doesn't go to A because you already have AB which is the same as BA)

B to D              BD

B to E              BE

B to F              BF

C to D             CD (C doesn't go to A or B because we already have AC and BC)

C to E             CE

C to F             CF

D to E             DE  (apply same reasoning as above)

D to F             DF

E to F             EF

there are 15 line segments that can be drawn

you could have drawn a circle with these points and connected the points to get the 15 line segments

however, you could gave done the following...

A connects to 5 points

B connects to 4 points

C connects to 3  points

D connects to 2 points

E connects to 1 point

F doesn't connect to any points because all the other points already connected to point F (same reasoning as above!!)

even if you had 10, 20, or 50 points you could easily get the answer by looking at the pattern that forms:

5,4,3,2,1

if you had 10 points the pattern would be 9,8,7,6,5,4,3,2,1

not knowing what level of math you are taking, this is the simplest way to see and get the answer

Answer 2

No matter where the points are on the circle, a line segment can be drawn connecting any two of these points. So the answer to you question is ₆C₂.....the combination of 6 things taken 2 at a time. this is equal to (6*5)/(2*1)= 15.

Hope this helped.