Question

Given three collinear points A,B,C with B between A and C, four different rays can be named using points AB, BA, BC, CB. How many different rays can be named given n collinear points?

Answer 1

Given n collinear points, 2(n -1) or 2n - 2 rays can be named

Explanation:

When we talk of collinear points, we mean points that lie on the same straight line.

For 3 collinear points we can have 4 rays

For 4 collinear points, let’s say ABCD

A B C D

The rays are AB BA BC CB CD and DC making a total of 6

For 5 collinear points,

A B C D E

The rays are;

AB BA BC CB CD DC DE ED which makes a total of 8

For 6 collinear points, we have;

A B C D E F

The rays are;

AB BA BC CB CD DC DE ED FE EF which makes a total of 10

So what pattern do we notice?

3 points 4 rays

4 points 6 rays

5 points 8 rays

6 points 10 rays

7 points 12 rays

So using the pattern

n rays = 2n - 2 rays or simply 2(n - 1) rays