PLANO CARTESIANO | Aprenda de uma forma diferente \Prof. Gis/

Hi everyone, welcome to another class on Gis' channel. And speaking of class today, I'm going to explain something that has everything to do with where you find yourself today. So, are you curious?

Want to learn more about this, then come with me. Before starting the explanation, I want to ask you those 2 things. You already know that Gis is going to ask, right?

Subscribe to my channel, like and share this video with your friends. This is to help us and hey, give us a thumbs up. I already said like, I didn't say, leave a thumbs up, don't forget people.

OK? And where in this world do you watch me from? Did you know that the location of any person in this world is determined by a system of coordinates called latitude and longitude?

You learned this in geography class, didn't you? I still remember in Geography classes that I learned this, look there, huh? Good.

Latitudes, so they are divisions that are based on the Equator and they are made from north to south, right? And the longitudes are based on the Greenwich Meridian, and they are divisions made from east to west. OK, guys, so you must have seen this in Geography class, so let's look at the map here so you can remember a little more about this content.

Come on, guys, let's look at the World map now, so we can identify the coordinates of any point, of a person who is located in a certain place, then look at the map I brought. If you observe what I said about latitude and longitude, I can identify what the coordinate of point A is, knowing that point A is located at latitude 60° north. And longitude 40° east, right guys?

And point c? Can you identify the coordinate of point c? Pretend it's a person who is there at the point and what is that person's coordinate?

So? So, we say that it is latitude 0° and longitude 20° east. You saw that it is right above the equator, right?

So can you now identify the coordinates of person B and person D? So I'll leave that there for you to do later, okay, guys? Did you understand how the coordinate system works?

So, when I look at the World map, I want to leave you with a challenge, do you know where in this world I am recording this class? Well, I'll give you a hint, so, my latitude is 23° South and my longitude is 51° West, so what? So, try to identify where we are talking about?

OK, guys, well, I told you about Geography here, which is where we also use this coordinate system, because our focus will be on mathematics, but I like to show the student where else, besides mathematics, I can use. Oh, and there's one place I didn't mention. Who hasn't seen a GPS before is one that has a cell phone app that takes us anywhere in the world.

It also works based on this coordinate system, latitude and longitude, OK? Now in mathematics class, we will work, then, on the Cartesian plane, which is the same system that we see in Geography class, looking at the World map, but now we don't look at the World map, we look simply for a plane that we call a Cartesian plane, that's it. And did you know why the Cartesian plane is called Cartesian plane?

It is due to a tribute to a mathematician René de Cartes, due to his studies and the things he identified he received this name, Cartesian plane. Not him, not the mathematician the Cartesian Plane. It got its name, okay, guys?

So, what is a Cartesian plane, then? That's what I'm saying so much, but I'm not saying that it's a Cartesian plane, it's made up of 2 axes that are perpendicular. Do you remember what perpendiculars are?

Perpendiculars are 2 lines that intersect and form 90°. Look at the drawing I brought, so for those of you who don't remember what perpendicular lines are, I'll leave you with the lesson instructions, agreed? So, here I have 2 axes, now here in the field of mathematics I will no longer talk about latitude and longitude, but rather, I will talk about axes, okay?

So I have this axis horizontally and this axis vertically OK? And they intersect here forming a 90° angle, okay? So, as I wrote here, so you have the definition.

A Cartesian plane is a region formed by 2 perpendicular axes as I already showed you here. The horizontal axis, so this horizontal axis, which is the axis that is lying down, is called the abscissa axis. Look at the name abscissa, I even wrote it in letters, it's capital letters here so you can see how it's written, okay, or x-axis, we're not going to keep talking about the abscissa axis all the time, I'm going to start saying x-axis, so the horizontal is the axis of the abscissa, which is the X axis and this axis that is vertical, which is upright, is called the ordinate axis or y axis, okay?

And the point where these 2 axes intersect, the point where it crossed is here in the middle, is called the origin of the Cartesian plane. So, right here, in this middle, I have the origin of the Cartesian plane, right, guys, look, I'm even going to mark here that this is our zero, where everything starts, okay? So, what do you need to know?

Depending on what level of education you are? You only study the Cartesian plane here, look, it's in this place here that we call the quadrant, okay? First quadrant, second quadrant, third quadrant and fourth quadrant, quadrant that is divided into 4 parts here, okay?

So, for you who are, for example, in the sixth year and who are watching gis, it is likely that you study the Cartesian plane only here, oh, in the first quadrant. Okay, and for you who are already in the seventh, eighth and other levels of education, you will also study in total, in its entirety here, well, how does it work then, a Cartesian plan. As I said here the origin, so it's our zero, this is where it starts here, so I'm going to divide it, then.

1 2 3 4 5. And he continues, and what you should notice is that you must have already seen that I didn't do it. It's just that the distance from one to the other here, oh, must be the same.

I already did it, it's wrong for you to say, but you didn't do it Gis, just so you realize that it has to be the same distance, okay? And here from scratch, right? As if it were a thermometer above zero, I also have, look, 1, 2, 3, 4, 5, you can see that there is a little arrow here indicating that they are infinite.

It's OK? So, for those of you who are at sixth grade level, you only study here in this region. OK?

And for those of you who are at other levels, seventh year onwards, you will study the negatives part too. So, here on the abscissa axis, which is the horizontal axis, you then have 012345 which are infinite. But before zero you have already studied numbers that are negative.

Did not study? So before zero I have. The minus one, the minus 2, the minus 3, the minus 4, and they are also infinite, okay?

And here now we're going to look at the vertical axis, which is the ordinate axis, the y-axis above the axis is the positive values. Below zero, here we have the values ​​that are negative, so I would have − 1, − 21, − 3 and so on. OK?

And one thing you must know to locate a point here on the Cartesian plane. So I'm going to have the ordered pair guys, and you need to mark this very big and nice so you always remember that you will not only use this ordered pair when doing a Cartesian plane exercise here, but in other mathematics contexts . It requires you to know what they are, what is actually a Cartesian plane, a Cartesian plane so it will always be a value that goes from XY.

In Geography class I talked about latitude and longitude, what would that look like? You can see, look at the X, that it is some point here on the abscissa axis, which is the horizontal axis it is representing in Geography class. Longitude is not that and our y, which is the ordinate axis, which is here in a vertical position.

It would be representing latitude, okay? So just telling you this identification, this comparison so that you can understand better, right? But then guys, if I had, for example, a square in a famous city, let's go, a square, I'll represent it by the point p.

And the ordered pair that represents the location of this square. Now I'm not looking at the world map, okay? I I'm looking at the Cartesian plane, here from Gis, right, it's pretend that it's points 1 and 2.

So guys, how do I identify this ordered pair of the square in my Cartesian plane, which is 1 and 2, well, that I always know. So, this first number here is representing the value of the abscissa axis abscissa axis 1, 1 is here, 2 is the ordinate axis that is representing Y, it is not always like this, X and Y, mark well there, oh, very big and beautiful. A very colorful post-it, okay?

So I would have to make the connection between these: 1 of And you, have you played Naval Battle? No, so I'm going to show you quickly how this game works and we also use the coordinate system. Huh?

Let's not talk about geographic coordinates here, are we talking about the Cartesian plane? Come on, guys, so when I play Naval Battle, this game consists of saying what coordinate you think your opponent's boat is at. Then you say a coordinate.

If you get it right, what is this coordinate, right? Whatever the actual location of your opponent's little boat, you can sink, so that little boat, OK, so onto this class. Okay, don't stop yet, listen to what I'm going to say, let me give you the instructions, you will then draw in the Cartesian plane.

Look for some squared paper at the end of the textbook, on paper you have squared or make a square in your notebook, okay? And then you will draw the little boat, remembering that it has to follow the guidelines of the Cartesian plan. A certain ordered pair , OK?

And then you do the same. Your colleague draws one, it always has to be a pair, right guys? Your colleague draws one and you try to guess what the coordinates of his little boat are to try to create beauty and then, if we were to play here in class now, what would be the coordinates where my little boats are located?

You see, you don't see, right? So you can try to guess, tell me what's your guess? What coordinates would you give to try to sink the Gis boats?

Remembering that I only placed 2 boats. Boat A, what is the coordinate then, what would you have to say to sink Gis' boat A? Remembering that I must obey the ordered pair, it would be a value of X and a value of y, abscissa and ordinate.

Well, so if we were to analyze, oh 01234, so here, from 4 to 5, I have a little boat, oh, so it would be abscissa 4 with ordinate 3, so, if you had said that little boat A was on abscissa 4 and on ordered 3, you could sink Gis's little boat, oh, okay, a little boat doesn't have to be just one square, it can even be 3 squares, right? Even I like to play when it's this Naval Battle game and what would be the coordinate, then, of the other little boat of the little boat b here, the little boat b, so I always look first in relation to the abscissa axis. Abscissa 5 negative, right?

And ordinate, minus 3 so, for you to sink the little boat b da gis, you would have to say abscissa minus 5 and ordinate minus 3, then you would be able to sink the little boat here, okay? So, just a simulation for you, of how the Battleship game works, OK, now we're going to try to locate some points, some points that I'm going to randomly place here and you're going to tell me? So what is the ordered pair that represents the location of this point there on my Cartesian plane?

Come on, guys, look, I brought here 4 flags, here I am, I'm going to place these flags here in my Cartesian plane, it's simulating that it's a square, another is a church, the other is a shopping mall and the other is what ? Could it be a football field? Damn, I already forgot the order, guys.

But anyway, then I'm going to place these flags here in my Cartesian plane. And you're going to try to guess, guessing won't identify, right? Because I will look there, it will identify which ordered pair represents this respective location.

So come on, Oh, I don't even remember the first one, so the square or not, I don't know. I'm going to place this first Flag here, oh, at this Point, and then can you identify what this location is? What is this ordered pair, oh?

5 which is on the axis because first I look at the axes of the abscissa abscissa. 5 then from the abscissa axis, o 5 and who is the ordinate axis? What is the value referring to the ordinate axis?

5 with 2, look, it's right on top of the line, okay? 5 and 2, so let's put it that represents Flag A, OK, let's even put it here, let me remove the Flag and put here Flag a o, Flag A which I don't even remember the order in which I said the places, but we Do it like this, Flag A. Now Flag B, let me put it here, Flag B, because I haven't written it already, right, guys?

Before I put it. Look, Flag B, stop there, Flag b. What then is the ordered parent that represents this location of Flag b Flag b?

So it is located, ordered and abscissa. What's the order, can I change it? I don't have to say abscissa first, so the abscissa is at minus 5 or minus 5 of the abscissa and what is the ordinate?

Let's look at the line here, look, the ordinate, minus 4, okay? Negative 5 and negative 4 so I will now place the Flag c. Oh, Flag c, let me see where I'm going to put Flag c, I'm going to put it right here.

Wow, let's not put it here, oh, right here, can you see the Flag and where is it? The Flag c is in which ordered pair, see the abscissa, guys, look, I'm going to remove a little bit, look, it's right here, look. She's right here, look.

Abscissa 4, it's here, right? So the abscissa will be 4 and what will be the ordinate? 4 with negative 3, o negative 3.

So let's put it back there. If not, you wouldn't be able to identify it, right, guys? And finally, I will place Flag d.

In the second quadrant I didn't put anyone there, so I'm going to put Flag d here, look, you can see where Flag D is located. Flag d is at minus 3 or minus 3 of the abscissa Flag d is located at least 3 and the ordinate which is U. OK, so here's how I can play a game so I can identify which are the ordinate pairs that represent the location on the Cartesian plane.

OK, guys, let's do one more example before finishing this class, come on, guys, now look, I have the 4 flags here again, look ABCD, but now I'm going to do the opposite process, I want to see if you understand Is this content ok? Then the. I already brought the locations here in the Cartesian plane, OK?

And, I need you to place the flags in their respective places. In fact, I'm going to put it to you, but you're going to give a recommendation to Gis, can you do it? The Flag must be in the ordered pair 0 and 2, remembering that zero refers to x, which is the abscissa axis, and 2 is the ordinate axis, where is the flag here, where does this Flag A go?

Tell Gis, where are you going? you are talking? So speak louder than me, I'm not listening yet, there is now, so 0 and 2 on the x axis because when it's zero people it means it 's going to be on top of the axis, so it's zero which is on top of the axis here, look , because where is the zero here?

Remember that I spoke about the origin, with the 2 of Y. So there will be zero of 2 is representing the point y 0 and 2. So that point is A, okay?

And 0 and 0 is the point b where even though it is this point, this coordinate 0 and 0 is right at the origin, guys, because it is right at the intersection of the 2 axes. So point b where the flag is here, I'm going to place it, right at the origin, which is where the axes cross, okay? 0 and 0.

Right, point c 8 and 0. 8 refers to the abscissa axis, which is the X, X Axis. And zero is the ordinate axis, so where is Flag c, guys?

Will it be on top of zero or 8, 8 of x or 8 of y Ah, the 8 of x? Look here, so Flag c will be on top of the 8 of x, 8 of x with zero of y. Is this how it's going to be OK?

So it is always on top of the value, because the other one is zero, that's good and the next −7, − 3, − 7 − 3. Let's see abscissa minus 7 is sorted here, minus 3 is here, so the Flag d she goes Is staying here ok guys? So one thing that students always have doubts about is when the cases are here like case A and case c.

It's OK? Students have doubts, it's normal, so you'll look here who is zero and X is zero. So, of course, a Flag has to be on top of the 2, which is related to y, so that's why I placed the Flag on top of the 2.

OK, and in this case here, whoever is the zero is zeroed in the y that number do I have? I have 8 of the x , so the Flag here was on top of the 8 of the x, it would be fine if it were, for example, 3 and 0, where would the Flag be here on top of the axis. Above dot 3 is fine, so whenever the ordered pair is like this, a value and a 0, the Flag is always above the value, different from zero, okay?

And whether it's in X or Y, you can identify it every time and the only time in fact, right? Guys, it will stay at the origin when its ordered pair is 0 and 0, agreed guys. So don't forget that when I talk about ordered pairs, I need an X value and a y value.

You can't change it, otherwise the location will be wrong. Agreed? Guys, I hope you understood this lesson.

You liked it, right? From the explanation I brought here for you about the Cartesian plane, it's good, and be sure to include in the comments the location I 'm talking about, remembering that I'm at latitude 23° south and longitude 51° west. Let's see if you can get Gis's location right, okay?

And, before finishing the class, say goodbye. Subscribe to Gis's channel, if you're not already subscribed and leave a thumbs up and see you in the next class, bye. .

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