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How many distinct rays are there given n collinear points?

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User Zuzlx
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1 Answer

4 votes

Answer:

(n * (n - 1)) / 2

Explanation:

If we have n collinear points, then we can draw n - 1 non-overlapping rays starting from any point on the line. This is because if we choose any two points on the line, then we can draw a unique ray passing through them, and since there are n choose 2 pairs of points on the line, we can draw n choose 2 = (n * (n - 1)) / 2 rays passing through them. However, each of these rays is counted twice (once for each of its endpoints), so we divide by 2 to get the final answer.

Therefore, the number of distinct rays that can be drawn from n collinear points is:

(n * (n - 1)) / 2

Note that this formula assumes that no three points are collinear, as otherwise, the number of rays would be infinite.

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User Msvcyc
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