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## Geometry (all content)

### Course: Geometry (all content)>Unit 1

Lesson 4: Points, lines, & planes

# Specifying planes in three dimensions

In a three-dimensional space, a plane can be defined by three points it contains, as long as those points are not on the same line. Learn more about it in this video. Created by Sal Khan.

## Want to join the conversation?

• What does collinear mean? •   Hi Pranav,
Collinear points are points that lie on the same line. If you only have two points, they will always be collinear because it is possible to draw a line between any two points. If you have three or more points, then, only if you can draw a single line between all of your points would they be considered collinear.
Hope that helps!
• I though a plane was two dimensional, if I am wrong can you please explain? •   Planes are two dimensional, but they can exist in three dimensional space.
• I don't understand what names a plane and why you need 3 points •   What is the smallest number of legs a stool can have and still be a free standing stool?

If it has one leg it will fall over... same with two.
If it has three legs it will stand, but only if those three legs are not on the same line... the ends of those three (non-collinear) feet define a plane.

If the stool has four legs (non-collinear) it will stand, but if one of the feet is out of alignment it will wobble... it wobbles between two sets of three legs each... each defines a different plane.

If I remember correctly you can identify a plane with a single capital letter, or any three non-collinear points in that plane... so if plane M contains points a, b and c it could also be called plane abc
• What do collinear and coplanar mean? •  Collinear means "lying on the same line". Two or more points are collinear, if there is one line, that connects all of them (e.g. the points A, B, C, D are collinear if there is a line all of them are on). This means, that if you look at just two points, they are automatically collinear, as you could draw a line that connects them.

Coplanar means "lying on the same plane". Points are coplanar, if they are all on the same plane, which is a two- dimensional surface. Any three points are coplanar (i.e there is some plane all three of them lie on), but with more than three points, there is the possibility that they are not coplanar.
• At he says collinear what does that mean? •  Let's break the word collinear down:

co- : prefix meaning to share. For example, a coworker is someone who shares your work place.
linear: related to a line.

If we put this together, collinear would mean something that shares a line. Or, points that lie on the same line.
• I'm slightly confused on the difference between the 1st, 2nd, and 3rd dimensions. i understand that they each identify how an object occupies space and how it can move in said space (ie; 1st can't move at all, 2nd can only move back and forth or up and down, 3rd can move forwards, backwards, up down, back and forth) but i don't get how i would use this or how it would work in higher powers such as the 4th or 5th and how we have come to understand we live in a universe of dimensions. • Be careful with what you said. A object in 1-dimensional space can move in exactly one direction. So really it's proper to say:

0D: I can't move anywhere.
1D: I can move in one direction.
2D: I can move in any combination of two directions.
3D: I can move in any combination of three directions.

For higher dimensions, we can't visually see it, but we can certainly understand the concept. For instance, an example of a 4D space would be the world we live in and the dimension of time. We can't see time, but we know that it is independent of the other three dimensions. Hope this helps. Good luck.
• why don't they show us what "coplanar" points in this video. If anyone saw it please tell ,and please explain it to me • I did not see "coplanar" within this video, but coplanar refers to points that lie on the same axis or plane as they keep mentioning. For example, if points A, B and C lie on the X axis, then they are coplanar. If, for example, line GF were represented diagonally, with an interception at point (0,0), and points DEF lie on line GF, then they would all lie on the same axis, making them coplanar.
• I am still confused about what a plane is. Is it any shape?   