In general, how many planes are there which contain (a) two given points, (b) three given points, (c) four given points?

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• Anonymous

a. two given points would lie on a line. An infinite number of planes could contain that line. They'd radiate out from that line like a barrel, sort of.

b. Only one plane could contain all three points. And the fourth given point (and fifth, and so on) would have to already be in that plane, so only one plane could contain all 4 points. However....

It is possible (if not likely) that three of the four points would be in the plane but the 4th one just isn't in it. So it could be that no plane could contain all 4 points.

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• In geometry, by definition, a plane always consists of 2 points. Think about a map on a piece of paper. You can only name 2 points to exactly point to where the place is on the map. Hope this helps.

Good Luck,

btw... Happy New Year

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• The excerpt below is from the second source given below:

In mathematics, a plane is a fundamental two-dimensional object. Intuitively, it may be visualized as a flat infinite sheet of paper. There are several definitions of the plane, equivalent in the sense of Euclidean geometry, but which can be extended in different ways to define objects in other areas of mathematics

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• try going to FAA.gov

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