For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

### The Coordinate Plane

#### Related Links

- Cartesian coordinate system
- Point
- Plane
- Positive and negative numbers
- Perpendicular
- Line
- Origin
- Dimension
- Hyperplanes
- Euclidean geometry
- Ordered pair
- Quadrants and octants
- Point

- The coordinate plane contains the x- and y-axes
- The x-axis and y-axis break the coordinate plane into four sections, called quadrants
- 1
^{st}quadrant: upper right - 2
^{nd}quadrant: upper left - 3
^{rd}quadrant: bottom left - 4
^{th}quadrant: bottom right

### The 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 0:05
- The Coordinate Plane
- Quadrants, Origin, and Ordered Pair
- The Coordinate Plane 7:02
- Write the Coordinates for Points A, B, and C
- Extra Example 1: Graph Each Point on the Coordinate Plane 9:03
- Extra Example 2: Write the Coordinate and Quadrant for Each Point 11:05
- Extra Example 3: Name Two Points From Each of the Four Quadrants 13:13
- Extra Example 4: Graph Each Point on the Same Coordinate Plane 17:47

### Basic Math Online Course

### Transcription: The Coordinate Plane

*Welcome back to Educator.com.*0000

*For the next lesson, we are going to go over the coordinate plane.*0002

*This right here is called the coordinate plane; it consists of two lines like this.*0008

*This right here, the horizontal line, is called the x-axis.*0016

*The vertical line is the y-axis; together they make up the coordinate plane.*0024

*Think of the coordinate plane as like a map.*0034

*It is a map; we are going to place points along this map.*0037

*We have to label each point based on the x-axis and the y-axis.*0042

*That is the coordinate plane.*0048

*These axes, the x-axis and the y-axis, break the coordinate plane into four sections.*0052

*One, two, three, four, those four sections are called quadrants.*0064

*The first quadrant is this space right here; this is called quadrant one.*0074

*Going over to this side, this is quadrant two; then down, this is quadrant three.*0086

*The last one is quadrant four; those are the four sections of the coordinate plane.*0097

*Each axis is numbered; it is labelled.*0108

*Here, this point right here is going to start off at 0.*0112

*It is going to go 1, 2, 3, 4, 5, and so on; 1, 2, 3, 4, 5.*0116

*Again this is 0; this way, then it is going to go negative.*0126

*See how it goes positive this way.*0133

*If you go the other way, it is going to go negative; -1, -2, -3, -4, -5, and so on.*0134

*Same thing for the y-axis.*0143

*If you go upwards, it is going to go positive.*0146

*It is going to go 1, 2, 3, 4, 5.*0151

*The arrows represent continuation; it is going to keep going on forever.*0158

*It doesn't just stop at 5; it is going to keep going.*0165

*Down this way, it is going to be negative; -1, -2, -3, -4, -5.*0168

*Next right here, a number on the x-axis paired with the number on the y-axis is going to give us an ordered pair.*0183

*You are going to look for the number on the x and the number on the y.*0198

*Together it is going to map out your location on the coordinate plane.*0202

*That point is called an ordered pair; it is going to be written like this.*0209

*In parentheses, you are going to have two numbers.*0216

*The first number is going to be your x number; that is called the x-coordinate.*0219

*The second number is going to be your y coordinate.*0231

*It is always going to be x and then y.*0239

*X always has to come first; (x, y) for short.*0242

*(x, y), that is going to be your ordered pair.*0247

*That is going to map out your location on the coordinate plane.*0252

*This point where the x-axis and y-axis meet, that is called the origin.*0259

*That is right there.*0267

*If you look at the x-number, the x-number, it is 0.*0269

*The x-number is 0; the y-number is also 0.*0275

*The origin is (0, 0); that is the ordered pair for the origin.*0280

*If I put a point right here on the coordinate plane, that ordered pair, what is the x-number?*0287

*If you look, this point is paired with an x-number and a y-number.*0301

*This point is going to have a x-number of 3 and a y-number of 1.*0309

*The ordered pair for this point is (3, 1).*0321

*Be careful that you don't mix those up, switch them up.*0324

*It is not (1, 3); that is not the same thing.*0328

*(1, 3), if I say (1, 3), because I said 1 first, that means I am talking about 1 on the x-axis.*0331

*(1, 3) would be 1 on the x; 3 on the y.*0341

*Where do they meet?--right there, that would be (1, 3).*0348

*(1, 3) and (3, 1) are not the same thing; be careful with that.*0352

*Always make sure the first number is your x-coordinate on the x-axis, the horizontal line.*0356

*The second number is your y-axis, the number on your vertical line.*0363

*That is the coordinate plane.*0369

*Again we have the x-axis, the y-axis; each of the four sections are called quadrants.*0370

*It starts off with this right here, quadrant one, quadrant two, quadrant, three, and quadrant four.*0379

*Remember when you are writing out the numbers, this number is always 0.*0385

*It is going to go positive to the right and negative to the left.*0392

*On the y-axis, positive when you go up, negative when you go down.*0396

*Everything together, the coordinate plane which is like the map, the ordered pairs, the quadrants,*0402

*all of this that have to do with these points, the plane, all that is called the coordinate system.*0408

*It is like a system of all these things together.*0418

*Again a coordinate plane, each of these are just marked for you.*0425

*We have three points, A, B, and C.*0431

*Here is A; here is B; here is C; we want to write the coordinates.*0435

*In other words, we want to know the ordered pairs.*0439

*Find the ordered pairs of A, B, and C.*0442

*We know that this is the x and that is the y.*0446

*Let's start with A, this point right here.*0451

*What is the x-number that makes up this point?--1.*0455

*What is the y-number?--1.*0459

*For A, my x-number, the number on my x-axis, is 1.*0461

*The number on the y-axis is 1.*0468

*The ordered pair or the coordinates for A is (1, 1).*0473

*I am just going to write... because this is the name of the point.*0480

*A is what that point is labelled.*0483

*You can just write it in front of that ordered pair.*0486

*Next is B; again I am looking for the x-number first.*0491

*The x-number, the number on this x-axis that makes up this B is -1.*0497

*The y-number, -2.*0505

*They are negative numbers; but it is fine.*0513

*You are just listing them out like that, same way as when you have positive numbers, (-1, -2).*0515

*The next one is C; the x-number for C is 2.*0525

*The y-number for C is -1.*0533

*Those are the coordinate for A, B, and C.*0540

*Let's do our examples now; graph each point on the coordinate plane.*0543

*The first one, A is (4, 2).*0549

*Remember this is the x-number; this is the y-number.*0554

*I am going to label this as x; this as y.*0559

*4, you are going to look for 4 on the x-axis.*0564

*4; this is -4; here is 4.*0567

*Then look for 2 on the y-axis; here is 2.*0572

*Where do they meet?--right there.*0575

*This is A; I can label that point as A.*0581

*Next, B is (-3, 0); the x is -3; the y is 0.*0586

*-3 on the x is right here; 0 on the y.*0596

*Where is 0?--0 is right there.*0602

*(-3, 0), that means I am not moving any up or any down because there is no y.*0606

*If the y was 1, I would have to move up 1.*0611

*If y was -1, I would have to move down 1.*0614

*But y is 0 so I stay here; that is my B.*0617

*Next, x, y; 2 is x; y is 1.*0629

*Where do they meet?--right there; that is C.*0636

*Next is (-4, -2).*0643

*-4 on the x is right there; -2 on the y is right there.*0647

*Right there, they intersect at that point right there; that point is called D.*0654

*That is it for this example.*0663

*The next one, write the coordinates and quadrant for each point.*0667

*It is like the same thing that we just did a couple examples ago.*0672

*First let's start with A; remember this is my x, this is my y.*0676

*Look for the x that makes up this point right here.*0682

*A is -1; that is my x; y is a -3.*0688

*We also have to state what quadrant it is in.*0698

*Remember that this right here, this section, any points that fall in this section right here is quadrant one.*0702

*This section is quadrant two; quadrant three; and quadrant four.*0709

*If a point is on let's say right here, that doesn't fall under any quadrants.*0720

*That wouldn't be considered quadrant one or quadrant four.*0727

*In that case, you are just going to say that it is on the x-axis.*0729

*Or in this case, if a point lands right here.*0734

*Then it is not in quadrant three or four; it is actually on the y-axis.*0739

*This quadrant, point A is in quadrant three; let's just say quadrant three.*0745

*B, point B is... x is 1, y is 2; (1, 2); that is in quadrant one.*0753

*C is right there; 3 as my x; -1 as my y.*0768

*That is in quadrant four.*0776

*D, x is -3; y is 3; that is quadrant two.*0780

*Example three, name two points from each of the four quadrants.*0795

*It is a little bit hard to do when you don't have the coordinate plane.*0801

*Let's draw out a coordinate plane.*0805

*We don't have to draw it too big because we are not going to be plotting any points.*0812

*Here is the x; here is the y.*0817

*I know this is quadrant one; quadrant two; quadrant three; and quadrant four.*0819

*The trick here is to figure out whether my x-coordinates are going to be positive or negative*0830

*and my y-coordinates are going to be positive or negative.*0840

*Quadrant one, if you look here, all the points that have this as my x and this as my y,*0843

*any points that pair up with this part of my x, that part of my y, is going to be in quadrant one.*0852

*I know that here as I get to these numbers, it is going to be positive.*0861

*This is +1, +2, +3, so on.*0866

*My x-coordinate is going to be positive; it is a positive number; positive.*0870

*My y-coordinate is also going to be positive because these are positive numbers here; positive, positive.*0878

*Any ordered pair that has a positive number paired with a positive y-number is going to be in quadrant one.*0888

*For quadrant one, I have to name two points.*0898

*Any ordered pair with a positive x, positive y, is in quadrant one.*0904

*(1, 2), that is in quadrant one; what else?*0911

*(3, 4), that is also in quadrant one.*0916

*Look at quadrant two; quadrant two, all points with this part of my x.*0920

*Those are my negative numbers.*0931

*A negative x with this part of my y is going to be in quadrant two.*0934

*Then when I list my points in quadrant two,*0944

*it is going to be a negative x number with a positive y number.*0948

*Does that make sense?--it is negative.*0955

*All these numbers are negative here.*0957

*This is -1, -2, -3; it has to be a negative x-coordinate.*0961

*Then paired with a positive y coordinate is going to be in quadrant two.*0968

*(-1, +2) is right there; it is in quadrant two.*0976

*Again negative x, positive y; (-3, 4).*0984

*Quadrant three, again any numbers or any ordered pairs paired with a ?x with this part of the y-axis.*0995

*That is negative also; negative and a negative is going to be in quadrant three.*1007

*This is going to be a negative x, negative y.*1014

*(-1, -2) here is -1; here is -2.*1020

*Another one, (-3, -4).*1026

*For quadrant four, again positive x; how about the y?*1033

*It is going to be any ordered pairs paired with this side and this side.*1041

*Positive x, negative y; positive x, 1; negative y, -2.*1045

*Positive x, 3; negative y, -4.*1056

*Those two points are going to fall under quadrant four.*1061

*The fourth example, we are just going to graph more points on this coordinate plane.*1069

*I didn't number them; go ahead and number them right now.*1075

*1, 2, 3, 4, let's go up to 5; -1, -2, -3, -4, -5; 1, 2, 3, 4, 5.*1078

*The first point, A; I know this is going to be my x-number; this my y-number.*1098

*0 on my x-number is right here; on this right here, 0.*1106

*3 on my y-number is right here.*1113

*That means my y is going to be 3 and my x is going to be 0.*1116

*Meaning I am not going to have -1.*1121

*I am not going to have 1 as my x; I am going to have 0.*1124

*It is going to be that point right there; this is A.*1126

*The next one is (-2, -1); -2 on my x; -1 on my y.*1132

*They meet right there; here is B.*1140

*C is going to be -5 and then 0 as my y.*1147

*Remember if my y is 1, I go up 1.*1154

*If my y is -1, I go down 1; right there.*1156

*But it is 0; my y is 0; that means I don't move up or down.*1161

*I stay put; that is my C.*1164

*My last point D is going to be 4 and -6.*1168

*-6 on my y-axis is right here; they meet right there.*1177

*That point is labelled D.*1187

*That is it for this lesson; thank you for watching Educator.com.*1195

1 answer

Last reply by: Khanh Nguyen

Fri Oct 2, 2015 9:53 PM

Post by Khanh Nguyen on August 1, 2015

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