Lines determined by 5 pointsDate: Sun, 13 Nov 1994 13:34:47 -0500 From: Anonymous Subject: geometry Can somebody please answer this question: How many lines are determined by 5 points, no three of which are collinear? Date: Sun, 13 Nov 1994 16:16:36 -0500 (EST) From: Dr. Ken Subject: Re: geometry Hello there! You probably already know that two points determine a unique line. So your question can be rephrased as this: "how many different ways can we choose two points from a set of five points?" Since no three of these are collinear, you won't end up determining the same line twice by choosing different points; i.e. looking at the problem this way will give you the right answer. If the points we have are A, B, C, D, and E, then here are a few examples of lines we could get by choosing two at a time. AB AC AD AE BC BD and so on. Do you see any good, ordered way to list all the different ways to choose two points from this set of five points? If you can list all such combinations, you'll have names for all the lines, and you can just count them up! I hope this helps. Write back if you need more help! -Ken "Dr." Math |
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