Question

A plane doen't always have noncollinear points because they can be a line right?

Answer 1

Is that the full question they ask?

Answer 2

Well not exactly. It asks if a plane contains at least three noncollinear points

Answer 3

Well 2 points are the min number of points needed to form a line

3 points are the min needed to form a plane (the 3 points can't fall on the same line if you want this plane to be unique)

Answer 4

But a line is considered a plane right?

Answer 5

So I'd say yes that a plane contains at least 3 noncollinear points

Answer 6

no, a line and a plane are 2 different things

Answer 7

no but collinear points are coplanar, so that means that not all planes have three noncollinear points

Answer 8

?? right

Answer 9

"not all planes have three noncollinear points" is incorrect as any plane is defined by 3 noncollinear points

2 points to define a line
3 noncollinear points to define a plane

Answer 10

"collinear points are coplanar" is correct because you can run a plane through those 3 collinear points

however, this plane is NOT unique because you can spin the plane around the line to get different planes

Answer 11

oh, wait so how come points that are collinear are coplanar....but you can't name planes by collinear points

Answer 12

imagine you have 3 collinear points that lie on a perfectly flat ground surface (say it's paved perfectly flat and level)

so one plane that goes through these points is the ground

Answer 13

but how do you name the plane that is made up of collinear points?

Answer 14

now imagine you put up a wall that is completely flat and vertical. The points will also run along the wall (they are on the base of the wall)

this is another plane (of infinitely many) that run through these points

Answer 15

you can't as my example is pointing out

having 3 collinear points does NOT uniquely define a plane

Answer 16

this page has a good video (which is short) that shows what I mean

http://zonalandeducation.com/mmts/geometrySection/pointsLinesPlanes/planes4.html

Answer 17

but then that means that collinear lines aren't coplanar if they can't make a plane

Answer 18

you mean "collinear points" right?

saying "collinear lines" makes no sense

Answer 19

ya collinear points

Answer 20

they are coplanar, the problem is that we can't say "these 3 collinear lines define a UNIQUE plane"

Answer 21

that video and my example above shows what I mean

Answer 22

oh!!!! thanks so much that was what I was looking for . thanks for your help!

Answer 23

you're welcome