Basic Math 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 negative0830

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