Question

Hiiii!!!!! x) Can somebody explain:
Through any three noncollinear points there exists [exactly one] plane? I also need to figure out a diagram. Can anyone help?

Answer 1

2 points create a line or rather a line is the intersection of many planes

Answer 2

3 points create a stable condition that can fit onto 1 plane

Answer 3

You can draw a line connecting any two points . Then you can imagine a plane containing
third point and the line

Answer 4

a 3 legged chair will always sit flat

Answer 5

So they are in one line?

Answer 6

noncolinear means not in a line

Answer 7

Or they intersect at a certain point?

Answer 8

points dont intersect do they?

Answer 9

3 points can create a surface, which is a plane

Answer 10

Ngeh....Idk...could you help?
Wait, so as long as they make an enclosed area then it is a noncollinear plane?

Answer 11

2 planes intersecting can form a line

Answer 12

3 noncolinear points form a stable plane

Answer 13

2 intersecting planes form a line. And 3 form a stable plane....what is a "stable" plane? What makes it stable?

Answer 14

4 points creates a 3dimensional frame work

Answer 15

what makes it stable is that 3 points can always fit on 1 plane evenly

Answer 16

4 points makes a condition that make it possible to lift off into another plane

Answer 17

2 points can fit on more than one plane

Answer 18

So they have a even distance from each point? Or equal sides? And 4 points means two planes can be together/interact/intersect with each other?

Answer 19

take 3 fingers and place them on any surface, do they teeter?

Answer 20

distance doesnt matter, as long as they aint in a line

Answer 21

Teeter?

Answer 22

...yeah, teeter; to rock back and forth, to sway, to be balanced in a precarious manner

Answer 23

Oh, ok. Yeah, they do not teeter. So it can be pretty much any # or points as long as the line is not straight?

Answer 24

3 points will ALWAYS fit in the same plane ... always.

have you ever sat in a 4 legged chair that wont sit "flat" ?

Answer 25

or at a 4 legged table that wont sit "flat"?

Answer 26

Nope. So, the # of points is irrelevant as long as it is......flat?

Answer 27

.... its hard to imagine someone not sitting at a table or chair that didnt sit flat :/

4 points creates a condition where 1 point can be "out of whack" with the others so that 1 point is in a different "plane"

Answer 28

3 points will always fit onto 1 plane .... 3 points will always define a flat surface

Answer 29

a pyramid is a shape that has 4 points right?

Answer 30

Yes, 4 points and 4 sides that meet at a "out of whack" point?

Answer 31

correct :)

when you sit a pyramid shape down, does it rest on all 4 points?

can you balance it on 1 point?
2 points?

Answer 32

No it does not rest on all four necessarily. It can rest on one and two points if you do it right.....right??? O___O

Answer 33

if your lucky perhaps :) but 1 point is very unstable; 2 points is just as unstable; 4 point doesnt work at all; it will always want to find 3 point to become stable

Answer 34

Because it's "flat" yes?

Answer 35

correct; and that "flat" property is what we refer to as a "plane"

Answer 36

Ok. Can I use your image/triangle for my hw example? Or should I try to make a new image?