anonymous
  • anonymous
How come if three points are collinear then infinitely many planes go through them?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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OakTree
  • OakTree
Hi again. If three points are collinear then we can draw a line that goes through them. And this line can be contained by a plane - infinitely many planes, in fact. Here's a drawing.
OakTree
  • OakTree
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OakTree
  • OakTree
This horrifying rendition of a supernova is actually the following: the point is the line from the side, and each of those lines is a plane. Since you can basically make a circle out of the planes, and we know that there are infinitely many points in a circle, we know there are infinitely many planes that we can draw like this.

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OakTree
  • OakTree
Makes sense? Regardless of my negligible artistic skill?
anonymous
  • anonymous
so does that mean that many planes can all be in one spot? or is it because planes all extend forever that they'd eventually hit those points?
anonymous
  • anonymous
or do they all intersect but can't overlap?
OakTree
  • OakTree
Think about it like this then. What's the intersection of two lines?
anonymous
  • anonymous
a point
OakTree
  • OakTree
Okay. And how many lines can go through a single point?
anonymous
  • anonymous
uhh.. a infinite number of lines
OakTree
  • OakTree
Right. So similarly, the intersection of two planes is a line, and there are an infinite number of planes that can go through a single line. If you ever get confused, kind of downgrade the problem like that.
OakTree
  • OakTree
Does THAT make sense?
anonymous
  • anonymous
yes thank you!!
OakTree
  • OakTree
Okay. Great.

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