SOLUTION: There are 10 identified points on a number line. How many possible rays can be drawn using the given points?

Question 1180225: There are 10 identified points on a number line. How many possible rays can be drawn using the given points?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

A quote from wolframalpha.com:

There are several definitions of a ray.
When viewed as a vector, a ray is a vector from a point A to a point B.
In geometry, a ray is usually taken as a half-infinite line (also known as a half-line) with one of the two points A and B taken to be at infinity.

Those two definitions will give you different answers to your question.

(1) With the vector definition above, each ray has two endpoints, so each pair of the 10 points determines two rays -- one in each direction.

The number of pairs of points is C(10,2)=(10*9)/(2*1)=45

ANSWER #1: 2*45=90 rays can be drawn using the 10 points.

(2) With the geometric definition above, each ray has only one endpoint. Since you need a second point to determine the direction of the ray, the 10 points on a line determine 9 rays in each direction.

ANSWER#2: 2*9=18 rays can be drawn using the 10 points.

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