Question

How come if three points are collinear then infinitely many planes go through them?

Answer 1

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.

Answer 2

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.

Answer 3

Makes sense? Regardless of my negligible artistic skill?

Answer 4

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?

Answer 5

or do they all intersect but can't overlap?

Answer 6

Think about it like this then. What's the intersection of two lines?

Answer 7

a point

Answer 8

Okay. And how many lines can go through a single point?

Answer 9

uhh.. a infinite number of lines

Answer 10

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.

Answer 11

Does THAT make sense?

Answer 12

yes thank you!!

Answer 13

Okay. Great.