Draw a line with 3 distinct points on it. Label each with a different letter. How many different
rays can you name using only the three given points?
You can name 6 different rays using the three given points.
For example, if the three points are labeled A, B, and C, the rays are:
1. Ray AB
2. Ray AC
3. Ray BA
4. Ray BC
5. Ray CA
6. Ray CB
Note that even though the first three rays appear to be duplicates of the last three, they are considered distinct because the order of the letters matters when naming rays.
Draw a line with 3 distinct points on it. Label each with a different letter. How many different
rays can you name using only the three given points?
(1 point)
8
6
4
2
The correct answer is 6.
To determine the number of different rays that can be named using the three given points, let's understand what a ray is. A ray is a part of a line that starts at one point, called the endpoint, and extends infinitely in one direction.
Given that we have three distinct points labeled with different letters on a line, let's assume the points are A, B, and C, arranged in that order. We can name different rays using these points by considering different combinations of endpoints.
1. Ray AB: This ray starts at point A and extends infinitely in the direction of point B.
2. Ray AC: This ray starts at point A and extends infinitely in the direction of point C.
3. Ray BA: This ray starts at point B and extends infinitely in the direction of point A.
4. Ray BC: This ray starts at point B and extends infinitely in the direction of point C.
5. Ray CA: This ray starts at point C and extends infinitely in the direction of point A.
6. Ray CB: This ray starts at point C and extends infinitely in the direction of point B.
Thus, we can name six different rays using the three distinct points on the line.