### Related Articles:

### Points, Lines and Planes

- All geometric figures consist of points
- A point is usually named by a capital letter
- A line passes through two points. Lines consist of an infinite number of points. A line is often named by two points on the line or by a lowercase script letter.
- A plane is a flat surface that extends indefinitely in all directions. Planes are modeled by four-sided figures. A plane can be named by a capital script letter or by three non-collinear points in the plane

### Points, Lines and Planes

A(1, 4) B( − 7, 10) C(9, − 2) D( − 15, − 4)

- Quandrant I ( + , + ), Quandrant II ( − , + ), Quandrant III ( − , − ), Quandrant IV ( + , − )

A(0, 0), B(1, 4), C( − 2, − 6), D( − 4, − 4)

D( − 4, − 6), E(0, 1), F( − 2, 3)

- Graph points D, E and F on the same coordinate plane as A, B and C.

- Points in Quandrant I are ( + , + )

- Points in Quandrant IV are ( + , − )

- Graph points A, B and the line passes through them on a coordinate plane.

- Graph a line that passes through A(1, 4) and B( - 2, - 4).

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Points, Lines and Planes

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- Points
- Lines
- Planes
- Drawing and Labeling
- Example 1: Drawing and Labeling
- Example 2: Drawing and Labeling
- Example 3: Drawing and Labeling
- Example 4: Drawing and Labeling
- Extra Example 1: Points, Lines and Planes
- Extra Example 2: Naming Figures
- Extra Example 3: Points, Lines and Planes
- Extra Example 4: Draw and Label

- Intro 0:00
- Points 0:07
- Definition and Example of Points
- Lines 0:50
- Definition and Example of Lines
- Planes 2:59
- Definition and Example of Planes
- Drawing and Labeling 4:40
- Example 1: Drawing and Labeling
- Example 2: Drawing and Labeling
- Example 3: Drawing and Labeling
- Example 4: Drawing and Labeling
- Extra Example 1: Points, Lines and Planes 10:19
- Extra Example 2: Naming Figures 11:16
- Extra Example 3: Points, Lines and Planes 12:35
- Extra Example 4: Draw and Label 14:44

### Geometry Online Course

### Transcription: Points, Lines and Planes

*Welcome back to Educator.com.*0000

*This lesson is on points, lines, and planes; we are going to go over each of those.*0002

*First, let's start with points: all geometric figures consist of points.*0010

*That means that, whether we have a triangle, a square, a rectangle...we have a line...*0017

*no matter what we have, it is always going to consist of an infinite number of points.*0023

*A point is usually named by a capital letter, like this: this is point A.*0030

*(x,y), that point right there, the ordered pair, is labeled A; it is called point A; that is how it is named--point A--by capital letter.*0037

*Next, lines: a line passes through two points; so whenever you have two points, you can always draw a line through them.*0051

*So, a line has at least two points; lines consist of an infinite number of points.*0061

*With this line here, line n, I have two points labeled here, A and B; but a line consists of an infinite number of points.*0070

*So, every point on this line is one of the infinite numbers; so we have many, many, many points on this line, not just 2.*0079

*A line is often named by two points on the line, or by a lowercase script letter.*0091

*The way we label it, or the way we name it: this is an n in script; I can call this line n, or I can call it line AB (any two points).*0096

*Now, this line has arrows at each end; that means it is going continuously forever, infinitely continuous.*0112

*It never stops; since it is going in both directions, I can say that this is line AB, or line BA; this can also be BA.*0126

*And this is actually supposed to go like this, AB; or it could be BA, because it is going both ways.*0140

*Line AB...now, when we say line AB, then we don't draw a line above it, like this, because,*0153

*when we say "line," that takes care of it; we don't have to draw the line, because we are saying "line."*0160

*Line AB or line BA...this can also be line n in script, or AB with a line above it--a symbol.*0167

*Next, for planes: a plane is a flat surface that extends indefinitely in all directions.*0180

*Planes are modeled by four-sided figures; even though this plane is drawn like this, a four-sided figure,*0187

*it is actually going to go on forever in any direction.*0196

*If I draw a point here, then I can include that in the plane, because the plane is two-dimensional;*0202

*so the points could be either on the plane...or it might not be.*0210

*But they are modeled by four-sided figures; and make sure that it is flat.*0218

*A plane can be named by a capital script letter or by three non-collinear points in the plane.*0225

*So, this whole plane is called N; we can name this N, by a capital script letter, or by three non-collinear points in the plane.*0230

*Here are three non-collinear points (non-collinear, meaning that they do not form a straight line):*0245

*it could be plane N (the whole thing is titled N, so it could be plane N), or it could be plane ABC: plane N or plane ABC.*0254

*Now, it doesn't have to be ABC; it could be plane BCA; it could be plane CBA, CAB...either one is fine.*0266

*Now, drawing and labeling points, lines, and planes: the first one here: we have a line.*0281

*Now, I know that this is kind of hard to see, because there is so much on this slide; but just take a look at this right here.*0290

*It is just the first part; this line is line n; I don't have two points on this line labeled,*0297

*so I can't name this line by its points; I can't call it line S; it has to be line n; that would be the only name for it.*0308

*So, S, a capital letter--that is how points are labeled: S, or point S, is on n, or line n.*0318

*I could say that line n contains point S, or I can say that line n passes through S, or point S.*0329

*Even if it doesn't say plane N or point S, just by the way that the letter is written,*0342

*how you see the letter, you can determine if it is a point, a line, or a plane.*0348

*The next one: l and p intersect in R; how do we know what these are?*0355

*It is lowercase and script; that means that they are names of lines, so line l and line p intersect in R.*0362

*It is just a capital letter, not scripted, so it is just a point, R; so l and p intersect in R; they intersect at point R.*0372

* l and p both contain R, meaning that point R is part of line l, and R is part of line p.*0381

*R is the intersection of l and p; line l and line p--R is the intersection of the two lines.*0391

*The next one: l (here is l, line l) and T...now, this might be a little hard to see,*0402

*but when this line goes through the plane, this is where it is touching; so think of poking your pencil through your paper.*0412

*Right where you poke it through, if you leave your pencil through the paper, that point where your pencil is touching the paper--that would be point T.*0429

*I know it is kind of hard to see, but just think of it that way.*0440

*So, line l and T, that point, are in plane P--a capital script letter; that is the plane.*0443

* P contains point T and line l; line l is just going sideways, so if you just drew a line on the paper, then that would be line l.*0453

*Line m intersects P, the plane, at T; this line right here intersects the plane at that point--that is their intersection point.*0465

*T is the intersection of m with P; T is a point; point T is the intersection of line m with plane P.*0482

*Your pencil through your paper--the intersection of a plane with a line--will be a point, and that is point T.*0495

*The next one: this is a little bit harder to see; I know that it is kind of squished in there.*0504

*But here we have two planes: this is plane N, and this is plane R.*0511

*We have a line that is the intersection of R and N; so if you look at this line, this line is passing through plane R,*0519

*and it is also passing through plane N; and on that line are points A and B.*0533

*OK, line AB...the reason why this is labeled line AB is because there is no name for this line; so you just have to name it by any two points on the line.*0544

*So, AB is in plane N, and it is in plane R; this line is in both.*0560

* N and R, both planes, contain line AB; what does that mean?*0575

*If this line is part of both planes, that means that the line is the intersection of the two planes.*0587

*Think of when you have two planes intersecting; they are always going to intersect at a line.*0592

*It is not going to be a single point, like a line and a plane; two planes intersect at a line.*0599

*We will actually go over that later; N and R intersect in line AB.*0605

*The line AB is the intersection of N and R; there are different ways to say it.*0614

*Let's go over some examples: State whether each is best modeled by a point, a line, or a plane.*0621

*A knot in a rope: the knot...if I have a rope, and I have a knot, well, this knot is like a point.*0627

*This one is going to be a point.*0637

*The second one: a piece of cloth: cloth--a four-sided figure--that would be a plane.*0642

*Number 3: the corner of a desk: if I have a desk, the corner is going to be a point.*0653

*And a taut piece of thread; this thread is going to be a line.*0664

*The next example: List all of the possible names for each figure.*0677

*Line AB: this line can be line n; that is one name.*0680

*It can be like that, line AB or line BA; it can also be BA in symbols, like that, or BA this way.*0694

*The next one: Plane N: this is one way to name it.*0716

*I can also say plane ABC, plane ACB, plane BAC, plane BCA, CAB, and CBA.*0721

*There are all of the ways that I can label this plane.*0746

*Refer to the figure to name each.*0757

*A line passing through point A: there is point A; a line that is passing through is line l.*0760

*Two points collinear with point D (collinear, meaning that they line up--they form a line):*0776

*two points collinear with point D, so two points that are on the same line: points B and E.*0785

*A plane containing lines l and n: well, there isn't a plane that contains lines l and n,*0800

*because this line l is not part of plane R.*0819

*How do we know? because it is passing through, so it is like the pencil that you poke through your paper.*0824

*It is not on the plane; it is just passing through the plane.*0832

*So, a plane containing lines l and n is not here.*0836

*If I asked for two lines that plane R contains, I could say plane R contains lines n and...*0842

*the other one right here; there is no name for it, so I can say line FC.*0866

*I can write it like that, or I can say and line FC, like that.*0876

*OK, the next example: Draw and label a figure for each relationship.*0881

*The first one is point P on line AB.*0890

*It is a line...draw a line AB; there is AB, and point P is on the line, so we can draw it like that.*0895

*CD, the next one: line CD lies in plane R and contains point F.*0910

*So, I have a plane; line CD lies in plane R (this is plane R) and contains point F; the line contains point F.*0918

*Points A, B, and C are collinear, but points B, C, and D are non-collinear.*0947

*OK, that means I can just draw a line first, or I can just draw the points first, points A, B, and C.*0953

*They are collinear, but points B, C (there are B and C), and D are non-collinear; so I can just draw D somewhere not on the line.*0968

*OK, so A, B, and C are collinear, but B, C, and D are non-collinear.*0979

*OK, the next one: planes D and E intersect in n.*0985

*Now, this is a line, because it is a lowercase script letter.*0990

*So, here is one plane; here is another plane; let's label this plane D; this could be plane E.*0994

*And then, where they intersect, right here--that will be line n.*1019

*OK, that is it for this lesson; thank you for watching Educator.com.*1029

0 answers

Post by Kevin Zhang on August 21, 2016

Hi Professor Pyo,

I was looking at the slide of drawing and labeling. On the second figure, shouldn't you say that l and p intersect AT R?

And for the first one, I was wondering if you could say S is an element of line n.

Otherwise, I love your lessons!

0 answers

Post by Chris DesRochers on June 22, 2015

Couldn't it be said that in extra example 3 question 3 "a plane containing lines (script) l and (script)n would be either the plane names by the noncolinear points ABE and/or perhaps DBA, or even ADE? If not, why isn't this an acceptable answer/or conclusion to the question given the constraints of the problem?

Thank you,

Chris

0 answers

Post by Noah Romero on June 7, 2014

Thanks

1 answer

Last reply by: Manuela Campos

Wed Apr 30, 2014 11:15 AM

Post by Manoj Devashish on March 25, 2014

In the third drawing and labeling example,I don't get how a line can intersect with a plane.

1 answer

Last reply by: Professor Pyo

Thu Jan 2, 2014 3:30 PM

Post by Delores Sapp on October 19, 2013

Will the points ( if there are 4) form a certain figure if they are coplanar? Can they be connected in some way so you can determine if they are coplanar?

0 answers

Post by Delores Sapp on October 19, 2013

How can you tell if 4 points are coplanar?

0 answers

Post by Shahram Ahmadi N. Emran on July 12, 2013

Thanks

1 answer

Last reply by: Professor Pyo

Wed May 29, 2013 10:06 PM

Post by Manfred Berger on May 27, 2013

Should the fact that there's a right facing arrow on the line in example 2 prompt me to call it line AB rather than BA?

0 answers

Post by Leili Reza on October 23, 2012

thanks,,,,,, best

0 answers

Post by Joseph Reich on June 15, 2012

In drawing and labeling example 3, you should mention that lines l and m do not intersect. It is unclear from the sketch.

0 answers

Post by Edmund Mercado on February 20, 2012

In the Drawing and Labeling slide, the upper edge of plane N needs to be dotted because it should be hidden behind the intersecting plane R

0 answers

Post by Corinne Lee on July 14, 2011

I LIKE IT.

1 answer

Last reply by: Mary Pyo

Fri Aug 19, 2011 11:35 PM

Post by Sayaka Carpenter on July 1, 2011

how can you have a point that is not in the plane, if a plane is continuous, and it continues for ever?

3 answers

Last reply by: Joseph Reich

Fri Jun 15, 2012 5:45 PM

Post by David Hettwer on January 12, 2011

For the 3rd problem ("a plane containing lines l and n"), you indicate there is no plane that contains lines l and n. Wouldn't plane ADB be an answer to that question? That plane is not drawn on the figure but it seems like it is a correct answer.