draw a line with 3 distinct points one it. label each with a different letter. how many different rays can you name using only three given points?
a 8
b 6
c 4
d 2
d 2
To draw a line with 3 distinct points on it, you need to position the points in a way that they are all along the same straight line. Let's name these points as A, B, and C.
Now, let's figure out how many different rays can be named using these three points.
A ray is a part of a line that starts at one point and extends infinitely in one direction. To create a ray, you need to choose one point as the starting point and another point as the endpoint to define the direction of the ray.
Since we have 3 points (A, B, and C), we can choose any 2 points to define a ray. This can be represented by the combination formula:
C(n, r) = n! / (r!(n-r)!)
In this case, n = 3 (number of points) and r = 2 (number of points needed to define a ray).
Using the combination formula, we get:
C(3, 2) = 3! / (2!(3-2)!) = 3! / (2! * 1!) = 3 / 2 = 3
Therefore, the answer is 3 rays can be named using the three given points.
d) 2