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### Coordinate Plane

- Coordinate plane: Contains the x-axis and y-axis
- The x-axis and y-axis split the coordinate plane into 4 quadrants
- The origin is at (0,0)
- Collinear: Points that lie on the same line

### Coordinate Plane

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

- Quadrant I ( + , + ), Quadrant II ( − , + ), Quadrant III ( − , − ), Quadrant 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.

*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

### Coordinate Plane

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 0:00
- The Coordinate System 0:12
- Coordinate Plane: X-axis and Y-axis
- Quadrants
- Origin
- Ordered Pair
- Coordinate Plane 2:59
- Example: Writing Coordinates
- Coordinate Plane, cont. 4:15
- Example: Graphing & Coordinate Plane
- Collinear
- Extra Example 1: Writing Coordinates & Quadrants 7:34
- Extra Example 2: Quadrants 8:52
- Extra Example 3: Graphing & Coordinate Plane 10:58
- Extra Example 4: Collinear 12:50

### Geometry Online Course

### Transcription: Coordinate Plane

*Hello; welcome to Educator.com.*0000

*This is the Geometry course; the very first lesson is on the coordinate plane, which should be somewhat of a review.*0002

*So, make sure to check out the other free lessons of the syllabus.*0008

*Let's begin: the coordinate system: the coordinate plane is part of the coordinate system.*0011

*This here is called the coordinate plane; right here, this is the x-axis, and this is the y-axis.*0020

*And these two make up the four quadrants of the coordinate plane.*0034

*If we were to label these, this is I, II, III, and so on; we know that if we go this way, we are going to be going negative; positive and negative.*0042

*Now, these axes make up four quadrants; the four sections of the coordinate plane are known as quadrants.*0063

*Here, this is the first quadrant, so this is quadrant I; around this side, we have quadrant II; this is quadrant III, and quadrant IV.*0073

*So, it starts here, and it goes this way: I, II, III, IV.*0085

*And for quadrant I, we have a positive; we are only dealing with the positive x-axis and the positive y-axis.*0091

*For quadrant II, we have a negative x-axis, and then the positive y-axis.*0100

*For quadrant III, it is negative x and negative y; quadrant IV is positive x and negative y.*0104

*Those are quadrants; make sure that you remember that there are four of them.*0115

*The origin is right there: this is known as the origin.*0120

*The origin is (0,0): the x is 0, and the y is 0--right where they meet, that is the origin.*0128

*And this is an example of an ordered pair: an ordered pair is when you have the x-coordinate paired with a y-coordinate.*0138

*And together, it is called an ordered pair.*0157

*So, if I have a point, (4,2), this would be an ordered pair; my x-coordinate is before, and then 2 would be my y-coordinate.*0161

*So, let's practice graphing using the coordinate plane: we are going to look for these points and write the coordinates.*0177

*Here is A, B, and C; for point A, we know that this is 0; this is x; this is y; here is 1, 2, 3, -1, -2, -3;*0188

*so for point A, we always start with the x-axis first; so the x-coordinate goes first, and that is 1;*0211

*and then what is my y? 1; that is my ordered pair.*0224

*For B: my x-coordinate for point B is -1, and my y is going to be -2; so here is (-1,-2).*0230

*And for C, it is 2 for my x and -1 for my y.*0246

*We are going to graph each of the points on the coordinate plane.*0258

*For A, I have (4,2); this is my x and this is my y; this is my x and this is my y.*0280

*So, I am going to go to positive 4 on this side: 1, 2, 3, 4; and 2 on my y is +2, which is there; (4,2) is going to be right there.*0289

*I am going to label that point A.*0305

*For B, (-3,0): x is -3, which is 1, 2, -3...and my y is 0; that means I do not go up or down anything--I stay right there.*0309

*OK, this is where y is 0; and this part right here is going to be B.*0322

*C: it will be 1, 2, and 1 right there for C; and then D is (-4,-2); OK.*0329

*OK, there are all my points on the coordinate plane.*0354

*One more thing to go over: collinear points are points that lie on the same line.*0359

*When we have points that line up--you can draw a line through those points--those points will be collinear.*0366

*And let's see if we have any collinear points here.*0377

*Well, if you remember from algebra, for slope, we have rise over run;*0380

*all of those have to do with a line and points, when we are graphing lines on the coordinate plane.*0387

*So, here we have A and C--we know that those two, or any two, points will be collinear,*0393

*because you can draw a line through any two points.*0401

*Here, I know that those three points, A, C, and D, are collinear, because they will be on the same line.*0406

*They lie on the same line, so A, C, and D are collinear.*0419

*If you want to double-check this, you can use what you learned from algebra; you can count rise over run.*0425

*Find your slope from D to C, and then from C to A; and it should be the same, and also from C to A and D to A.*0433

*OK, so points A, C, and D are collinear.*0441

*Write the coordinates and quadrants for each point: let's look at point A.*0455

*Point A: this is -1, and my y is -1, -2, and -3; so for A, -1 is my x-coordinate, and -3 is my y-coordinate.*0464

*And this is quadrant III, because it goes I, II, and III; so this is in quadrant III.*0484

*For B: my x is +1, and my y is +2; and that is in quadrant I.*0494

*C is 3, and my y is -1; and that is quadrant IV; D is -3, and 3; quadrant II.*0507

*OK, let's do another example: Name two points in each of the four quadrants.*0530

*OK, we have quadrant I; now quadrant I, I know, is here; quadrant II, quadrant III, and quadrant IV.*0536

*Quadrant I is going to be positive, and then my y-coordinate is going to be positive.*0549

*Quadrant II: my x (x is always first), we know, is negative; and then y is positive.*0558

*Quadrant III is negative for the x-coordinate and negative for my y.*0568

*Quadrant IV is positive and negative.*0575

*They should all be different; their signs will be different for each of the quadrants.*0578

*So, I can name any point; as long as my x-coordinates and my y-coordinates are both positive, they are going to be from Quadrant I.*0583

*I can just say (1,2) and then maybe (3,4); those are two points from Quadrant I.*0592

*Quadrant II will be...we have to have a negative x-coordinate and a positive y-coordinate, so what about (-1,2) and (-3,4).*0602

*Now, you can use your own numbers; you can use the same numbers.*0619

*As long as you have a negative x and a positive y, they are from Quadrant II.*0625

*Quadrant III: x and y are both negative, so (-1,-2) and (-3,-4) will be from Quadrant III.*0630

*And then, Quadrant IV: we have a positive x and a negative y, so (1,2) and (3,-4).*0642

*Those are two points from each of the four quadrants.*0655

*The next example: Graph each point on the same coordinate plane.*0659

*Let me do these: the first one, point A, is (0,3).*0663

*Now, be careful--this 0 is my x; that means, on my x-axis, I am going to be at 0, which is right there.*0685

*And then, for my y (I'll just write out a few of these numbers: 1, 2, 3, 4, 1, 2, 3...OK, let me erase that...-3 and -4; OK)...*0698

*again, it is 0 for my x, and then 3 on my y; so there is 3 on my y.*0725

*And that is going to be my point A.*0735

*For point B, I'll go to -2 on my x and -1 on my y; there is B.*0740

*C is -5; there is -5 on my x and 0 on my y; that means I am not going to move up or down; I am going to stay there; there is C.*0748

*And then, D will be 4, and then -6 is all the way down here; so there is point D.*0758

*And my final example: Point A is (3,1) and B is (0,-5); they both lie on the graph y = 2x - 5.*0771

*Determine whether each point is collinear with points A and B.*0781

*OK, if I have my coordinate plane, my x- and my y-axis, my point A is going to be (3,1); there is A.*0785

*B is going to be (0,-5), right there; there is B.*0802

*They both lie on the graph y = 2x - 5; so if I draw a line through these points, that is going to be the line for this equation of y = 2x - 5.*0812

*And you are just going to determine whether each point is collinear with the points A and B.*0832

*Now, "collinear" means that they are going to be on the same line.*0837

*So, we are just going to see if these three points (since we know that points A and B are on this line) are going to also be on the line.*0841

*And if they are, then they will be collinear with the points.*0852

*For point C, instead of graphing the line and seeing if the point lies on the line, you can just...*0858

*since you know that this is x and this is your y, you can just plug it into the equation and see if it works.*0866

*y = 2x - 5: you are just going to plug in -1 for x and 4 for y.*0874

*So, 4 = 2(-1) - 5: here, this is 4 = -2 - 5; do we know that...since we don't know that these are equal...does 4 equal -7?*0880

*No, it does not; so this point does not lie on this line; that means that point C is not collinear--this says no.*0906

*OK, for point D, I am going to also plug in: 7 is my y; 7 = 2(6) - 5.*0918

*OK, I am going to put a question mark over my equals sign, just because I am not sure if it does yet--I can't see if it equals.*0940

*This is 12 - 5; 7 = 7, so this is a yes--they are collinear points.*0947

*And then, my last point, point E: -15 = 2(-5) - 5): put a question mark again.*0958

*-10 - 5...-15 does equal -15, so this is also a yes; OK.*0972

*Points D and E are collinear with points A and B, since they are all on the line y = 2x - 5.*0984

*That is it for this lesson; thank you for watching Educator.com!*0998

0 answers

Post by Kirnvir Kaur on August 25, 2015

I cant seem to find any videos about coplanar and noncoplanar

0 answers

Post by Arvind Ganesh on January 15, 2014

AMAZING!!!!!

1 answer

Last reply by: Eid Ismail

Sun Feb 15, 2015 12:49 PM

Post by Marisol Espinosa on August 10, 2012

cool!!!

0 answers

Post by Chudamuni Dahal on July 24, 2012

what a cute teacher teaching very clearly!!!

0 answers

Post by Sheila Mckenzie on June 8, 2012

Awesome!

1 answer

Last reply by: Eid Ismail

Sun Feb 15, 2015 12:49 PM

Post by Kang-Il Kim on June 4, 2012

I know = and/over= 's meanings but is

?

= real

0 answers

Post by alejandra montes on May 15, 2012

very good instructor ... everything is explained from beginning to end.. awesome!

1 answer

Last reply by: Kang-Il Kim

Mon Jun 4, 2012 11:52 AM

Post by IVAN STRICKLAND on January 31, 2011

Awsome.