BassamS471398 BassamS471398
  • 03-11-2022
  • Mathematics
contestada

How many lines are determined by 18 points, no 3 of which are collinear?

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LaelW718365 LaelW718365
  • 03-11-2022

First, consider the 3 points, no 3 of which are collinear; as shown in the diagram below

As one can see, we can form 3 different lines, lines 12, 13, and 23 (this is 2+1=3).

Similarly, in the case of 4 points,

There are 6 possible lines when considering 4 points on the plane (3+2+1=6).

Finally, in the case of 5 points on the plane,

4+3+2+1=10 lines when 5 points.

Therefore, for 18 points, there are 17+16+15+14+...+3+2+1=153

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