Class 9 Maths Chapter 1 | The 2-D Cartesian Coordinate System | Orienting Yourself | NCERT

Added: 2026-05-25

[00:00:00]Hello students, just imagine if you go to an unknown city and you do not know its location and your friend is coming to pick you up, neither do you know the roads nor the buildings, then what will you tell him on the phone, hey I am here, where is this, this is not going to work, right, that is why there are maps and locations in your phone, every single thing works with a proper system, when you play a game, even in that you get to know where is this point, where is that point? So every single thing has its exact location and a hidden system is working behind it and the interesting thing is that it is not there right now. This has been going on for many years.

[00:00:48]Mathematicians have been working since the very beginning.

[00:00:53]How can we know the location of any thing? So in this chapter we will learn how lines and numbers together tell the exact location of any point, object or person.

[00:01:04]And here we don't have to do any ordering.

[00:01:07]This is a coordinate system which tells us how we can find the exact location of something with the help of lines and numbers. And most importantly, if you understand coordinates very well, then you will be able to do graphs, maps and geometry very easily. So what are you waiting for? Let's start. But keep this in mind that we should not do it in order.

[00:01:34]We have to understand things. What is a graph? If you did not understand properly in the lower classes, then it does not matter. We will start from the basics here as well.

[00:01:44]So let's get started. So let's start. Orienting Yourself The Use of Coordinates. So where are coordinates used? So first of all you can see here that the directions are made here.

[00:01:58]Ok? East, West, North, South.

[00:02:01]So whenever we move anywhere, the most important thing for us is the navigation there. How are we getting there? To reach a place. Ok? It is very important to use coordinates to reach a particular place.

[00:02:18]Ok? And for that, you get the wishes and directions right there. Ok? If I assume it is a simple thing, I tell you to go ahead and take a left turn and go a little further and there you will find the shop you were looking for. How little, how little, what has been quantified, that thing has not been quantified, how little, one step, two steps, three steps, four steps, how much, so there only we use coordinates to reach each and every thing in the proper way.

[00:02:54]Ok?

[00:02:57]So this is your introduction that to know the exact physical location of any point or any object, we use coordinates. So where was it first used? Indus Saraswati Civilization.

[00:03:13]Look, now you will not feel for a long time whether we are studying Maths or History.

[00:03:18]Many children have also started speaking like this.

[00:03:20]But when we do math, you people have this question. Hey, where is maths used in daily life? Some are doing some other work. Ok? Suppose someone becomes a businessman. Now he is working in handlooms. Ok? So he will say, hey, how did it help me? Pythagoras. How did it come in handy to me? Where did all these things plus minus come in handy?

[00:03:42]But if we see, we are using maths everywhere in daily life.

[00:03:46]And as we start these chapters, they will tell us our history as to where we use each and every thing. Where have we been using it from and where are we using it now?

[00:03:57]So all these jokes that were made on maths, where do we use it in daily life.

[00:04:02]So for that, a special introduction has been given as to where we used it and when and where we will use it in future.

[00:04:11]So don't consider this thing boring. This thing has to be understood in an interesting way so that you become more interested after reading the chapter. Ok?

[00:04:18]So first of all, Indus Saraswati Civilization, you know that when we studied history, we had told that the first civilization was civilization, meaning when people gathered where a lot of people started living together. So the first civilization was your Indus Saraswati civilization. It was very modern. It was there that the first systematic use of grid was made.

[00:04:40]What is a grid? Grid means proper boxes. Now, how did they use this grid? Look, the city center has been made one here. Ok? Then he assigned directions: East, West, North, South. Ok?

[00:04:57]What now? If you want to find any shop, go to any place, then every place that was there was 10 cm. 10 sorry 10 meters 10 meters 10 meters 10 meters apart. So if anyone was standing here, he could easily tell them to go towards the east at a distance of 30 meters.

[00:05:16]Go East for 30 meters.

[00:05:19]You will get it there. Suppose someone is standing here, he will say go to the center and go to the north. Ok? Go to the center and go north. 10 cm So go to the center and go north 10 cm. He would reach exactly. So in this way, in a very systematic way, he used this thing in the grid. Ok? After that a different mathematician came to Budana. Ok? He used the East, West, North, South directions for geometric constructions, to build huge buildings. And Budana Pythagoras theorem was also developed.

[00:05:52]Ok? What is Pythagoras Theorem?

[00:05:55]Everyone knows. Ok? After that, Foundation of Coordinate Geometry also came out.

[00:06:00]We will now study what coordinate geometry is.

[00:06:02]Ok? And this is very important for navigation. Now suppose you people also use Google. Use Google Maps. Isn't it? Head North, East, West, right? She speaks like this. What it means is that you move ahead towards the East and after reaching there you have to take a turn towards the North or South or West. Ok? So in this way, whatever thing is there, it tells you the directions everywhere and the meaning of coordinate geometry is also that how can we measure it.

[00:06:36]How far do I have to go? 10 meters, 100 meters, how far do I have to go? Ok? And what was there before? Earlier Central Longitude Margin It was Ujjaini. That means you hear Ujjain in today's time. Ok? What was it?

[00:06:51]Like the map of India.

[00:06:56]Ok? This is the map of India.

[00:07:03]Ok? So here on this side, this line is formed in this manner, East, West, North, South.

[00:07:11]Where does this line originate from? It comes out from here. This thing comes to your Ujjain. Ok? Ujjain. At that time it was called Ujjaini. He was called Jaini. And now today we call it Ujjain. So this longitude which used to come earlier used to come from Ujjain side.

[00:07:26]Ok? Later we used to call that line as Ujjaini line. Ok?

[00:07:32]Later came latitudes, latitudes and longitudes. And Ujjain was also included in these longitudes.

[00:07:40]Ok? Then came Aryabhatta. He calculated the coordinates. The Coordinates of the Stars and a City.

[00:07:49]To tell the location of any star, to tell the location of any city, they used the coordinate system. Then came Brahmagupta.

[00:07:56]What did Brahmagupta do?

[00:07:58]Explained the modern coordinate system. What is origin? What is the negative axis?

[00:08:02]Told all these things. So now let's read quickly.

[00:08:04]We learned so much. Many more mathematicians came. He also did a lot of searches. After doing research, he realized that it is very important to know everything, to know the location. So what are coordinates? What is the origin? We know all this. Now, first of all, we have studied till now, we have studied the number line. Isn't it?

[00:08:28]Number line. What did we read when we studied the number line? I already told you one thing long ago that if we draw a line in this manner. Ok? Here I assume we have zero in the center. Ok? If we go this way, here we write positive integers here. 1 2 3 4 5 6 Write positive integers. If we go to the left side of zero, we write negative integers. -1, -2, -3, -4, so we had studied this number line. Ok?

[00:09:03]So whenever we are walking on a particular line, simply on a single line, then we call it 1D. 1D is one dimensional, that is, we are moving on a line.

[00:09:14]Is this clear? Ok? Ok.

[00:09:18]After that, this line comes to you. I will leave this line here. And if I mention this line here also. Like for example this is 0 1 2 3 4 5 -1 -2 -3 -4 -5 and if I pick up this line and bring it here, then that here is 1 2 3 4 5 and so on, it keeps going on without stopping at just five.

[00:09:48]Arrow means it is moving. Ok? Then down here it goes -1, -2, -3, -4, -5 and so on. Ok? Now what is this thing? This is called two dimensional. This is called two dimensional. What's inside it? Suppose here you are walking in a straight line. Now suppose you are walking anywhere. So I can tell where that guy is standing. How? Let's see. First of all, see what is this? This is your x axis. Ok? This is also called x axis.

[00:10:23]Ok? This is the x axis. And this is the y axis.

[00:10:29]Ok? what happens now? We call these coordinate systems. Ok? What do you say? Coordinate system. Now this happens right in your center. We call this origin.

[00:10:40]Origin. Origin is zero zero. Ok? That your x is also zero and y is also zero.

[00:10:46]What is your point here as well? It is just zero. Ok?

[00:10:49]So this is the origin.

[00:10:51]So here the origin is in one dimension, so it will remain one. There is one zero. Will you keep moving forward or how far have you progressed? Five have moved ahead.

[00:10:59]How far back have you gone? You have gone three times behind. Got a minus for the rear. So we are talking about one line.

[00:11:04]But if you went to a slant. Suppose you have reached here. So how far have you walked? Ok? Suppose you go straight from here like this. Ok? So how far have you reached? So you'll see how much was on your x side. On the x side was your two here and how much is on the y side? Two. So let's say if point is your a. Ok? So how do we mention this? Let's mention this. Let's write x first. Then we write y. Ok? So what are the coordinates of x? Two. And what are the coordinates of y?

[00:11:42]Two. Ok? So this is how we created its coordinates. So, in a way, this becomes the position that if a person has gone from here to here, then where is he at this time? He is lying on two two. That is, to is to from to from the x axis and to from the y axis. Is this clear? So this is the coordinate system. Ok? So this is about positive. There is also a negative one. This is negative from here. If in negative, suppose a person goes here and is here.

[00:12:14]Ok? Some guy went from here to here. Now you have to see its coordinates. So look at its coordinates, where is it going on x? This is going to x at -2. So first we write x, right? So let's say this is your point b. Write x first.

[00:12:33]What is x? - How much is 2 and y coming to? Look at y, here y is coming, your three, so this is three, it is clear, okay, after that the same thing is here, your negative axis, this is called negative axis and this is positive, this is positive axis, this is negative axis of y, the same thing is here, suppose it is here, okay, so now see how much is there on x, it is -2 on x and how much is there on y? -4 So what will we write? First x then y, so suppose this point is your c, then what are the coordinates of c?

[00:13:18]-2 -4 ok? Similarly, suppose this is a point here. Ok? So look at x, how far is it from x? is 5 away from x and how far is it from y? -4 So let it be point d so x is 5 and y is -4 So what can you do with anything like this? You can point out the location. You can know the location after knowing the coordinates. Ok? Once you know the coordinates, you can know its location. Ok? Also let me tell you one more thing.

[00:13:52]Whenever there are axes, this is the x axis, this is the y axis, positive axis, negative, positive, negative. This is origin. The origin is zero zero. That means here x is also zero and y is also zero. Ok? Now look at one thing here. This portion, now you will see that this thing has been made like this. Isn't it? I will show you this on the next page.

[00:14:23]This thing is yours like this. Now this is the x axis, positive this is the negative x axis, positive this is the y axis, negative this is the y axis. So this portion is called first quadrant. This is the first quadrant.

[00:14:47]We call this the first quadrant. Then reach here. We call this the second quadrant.

[00:14:56]And This Is Third Quadrant And This Is Fourth Quadrant. Now what is a quadrant? Quadrant is a fourth part. So if you notice this whole portion is one. This 1/4 part, this 1/4 part, this 1/4 part and this 1/4 part. Ok? So 1/4 of the complete is first. This is the first quadrant, this is the first part, this is the second part, this is the third and this is the fourth part. Now here you will notice one thing that in the first quadrant both x and y were positive. +x + y In the second quadrant you will notice x was your minus and y was your plus. You will notice in the third quadrant that both were negative. -x - y In the fourth quadrant you will notice that x was positive and y was negative. Are you getting the point? So x positive above this line below this sorry y positive below this line y negative. From this line to the right, x is positive, from this line to the left, x is negative. Is this clear? Ok? So this is your quadrant. After that, as we call it two dimensional, we basically have to study about it. So does this happen only in two dimensions? No. It is also three dimensional. There is also 3D.

[00:16:20]Like right now you're just looking at who? You are watching it now. You have a mobile in your hand.

[00:16:25]So you're looking at a screen.

[00:16:27]So you're seeing everything as one page.

[00:16:29]But if you look ahead wherever you are sitting, you will be sitting in a room only. If you look at any corner of the room, what will you see there? In a way, there is a wall here too. There is a wall here too. This is the floor. Suppose this is the floor. Ok? And the height, from here you will be able to see the height and there will be a roof above. Isn't it? That means you can see the length, width and height here also. That is, when you can major three things. Ok?

[00:17:06]What happened just now? That slant was going on. Suppose something moves after flying a little. That means his length, breadth and height have also increased.

[00:17:13]Ok? So what do we say in that case?

[00:17:15]Three dimensions. So how do we denote three dimensions as major? This is the x axis.

[00:17:21]Ok? This is your y axis from here and we find its slant like this.

[00:17:28]This is the Z axis. Ok? Where does its negative go? Its negative goes here.

[00:17:34]Its negative goes here and its negative goes here. Ok? So this is your three dimensional. Now if you notice this carefully, you can see it in any corner of any room. So you will see a height in the corner of the room. Front wall, left wall. So this is a three dimensional thing. So when your length, breadth and height also come there then it is 3D.

[00:17:58]So this is called 3D, there are three dimensions.

[00:18:00]But here I will also tell you the system of writing.

[00:18:05]If there is any point for writing then x, y and z also come along with it. Ok? But this is not in your syllabus right now. Right now there is only two dimensions in your syllabus. So right now we will focus on two dimensional first of all.

[00:18:17]Ok? So now to understand this two dimensional thing, see what has happened.

[00:18:24]Basically, you have also been given normal situations in the books so that you can understand those things and now you will say, hey, what do we have to do after understanding these X and Z? So for that you have been given a situation on daily basis.

[00:18:38]Ok? What about your normal life? So what is that situation? Let's discuss it once.

[00:18:42]So that situation is that there is a mother.

[00:18:45]Ok? What happens to them again and again? Posting continues. Postings keep happening from one place to another. Ok? They have two children. Ok? There is one girl. Ok? The girl's name is Shalini.

[00:19:07]And there is another boy.

[00:19:10]Ok? Whose name is Ryan.

[00:19:13]Ok? Now Ryan is not blind.

[00:19:17]He can't see. Ok? So when the mother gets posted again and again, she has to change her house again and again. Now we have to change it again and again. Look, if a child is living in the same house for a long time, then he comes to know that the washroom is on the left. You can go right and exit. There is a door here and there is a kitchen here. Ok? But when there are frequent postings, they have to change their house.

[00:19:40]So due to which it takes time for Ryan to understand the things around him. So what did Shalini use for that? Shalini used a map. Ok? He made a map and used a coordinate system in that map so that I could tell my brother clearly about his room, that if I go three steps ahead, this is it. If you come four steps back then this is it. So basically what did he do? He got a map created. Now see what a map is? Now what will the map maker do here? She will tell you by making the room smaller in size. Many times you tell your friends about your home, so how do you tell them? Hey, there's a street from here. If you go into the street here, you will turn left. We have one or two third houses here. You tell me like this, right? You explain it this way. So this rough thing that you made, it was made small, right? Ok? Is this clear? So I did not make the actual size and show it. So what did Same Shalini do? Shalini also made one on the map. And what scale did he put on the map? He kept 1 cm for 1 foot.

[00:20:50]Meaning, you know how big 1 foot is.

[00:20:53]How much is one foot? Near about, you can see the size from your hand to your elbow.

[00:20:57]So this is approximately one foot.

[00:21:00]Ok? So when we create this on the map, what happens inside it like this? 1 1 cm The distance is only. So 1 cm. 2 3 4 5 So he plotted 1 foot here on the map as 1 cm. He made it to Major. And he made the map very beautiful. Let's look at the map. So this map of Ryan's room has been created by Shalini.

[00:21:24]Ok? So what's in Ryan's room? So first of all you will notice that you will see a bed here. Ok? There is a bed and a lamp is placed next to the bed.

[00:21:35]Ok? And if you come to this side of the bed, there is a door here also. There is a door here too. There is a wardrobe here. Ok? It is his cupboard.

[00:21:46]Ok? There is a port installed here. The bedroom is 12 feet * 10 feet. Whenever it is written like this 12 * 10, 12 means your length and 10 means width. So length and width. Ok?

[00:22:02]After that, if there is a door here, then go here through this door, go inside and this is the bathroom. Ok? There is a bathroom. This is the bathing area. This is the bathing area, bathroom and exit from here. Here's to going out.

[00:22:16]Is the matter clear? So he has created this kind of map so that I can explain it to my brother very well. Now this map, he has created the same map on an A scale. That is, 1 cm of 1 foot. It is drawn on the x and y axis. And with whose help was it made? With thread, with a ruler.

[00:22:39]Ok? So that he can touch her. He can feel it by touching it and know how far this thing is from here. Ok? So he used thread, scale, ruler and he made this 1 cm. At a distance of. Let's make that once. So he created this thing.

[00:22:57]That means here you can see the x axis, here the y axis and this door, he placed the origin on this door.

[00:23:06]Ok? Placed the origin here.

[00:23:09]Here is his left wall. There is a right wall here. Now see what I said, what was written in the room? It was written 12 * 10. That means what is 12 to you?

[00:23:20]Your length is 12 and what is your width?

[00:23:24]10. So you'll notice here. Like I taught you coordinates. So there you can see the coordinates that here at this point you can see that it is written 12 * 10.

[00:23:33]So what does 12 mean? Your x axis length and how much did you get? y axis. The y axis is this.

[00:23:43]Ok? So, how much did you get? 10. Ok?

[00:23:47]Okay, now that I understand this thing, I will ask you some questions. Suppose I say, hey, the wardrobe is so big.

[00:23:54]How big is the wardrobe? What is the length of his wardrobe? So you see how long the wardrobe is. It is coming from here to here.

[00:24:02]Coming from three to seven.

[00:24:04]So let's count. This is the forest.

[00:24:07]This is how it is measured.

[00:24:16]1 2 3 4 Four units. Ok? Now why am I saying units? Because if I talk about scale, here we have 1 cm. It is kept at a distance of. And how much has he kept in real terms? On foot. Isn't it? So the length of 1 2 3 4 feet is the length of the wardrobe which is 4 feet. Ok? How much is it in real life and on the map? 4 cm So we can look here and say it is 4 units also.

[00:24:44]If you ask in real, how much is it in real? So will you tell me how much is there in it? It is 4 feet. Ok? Ok.

[00:24:52]Now the bed, how big is the back of the bed?

[00:24:56]So how much is the back of the bed? 1 2 3 1 2 3 3 feet. Ok? Now if I say from here that he opens that door from here.

[00:25:07]So how far is the bed from the door? So how far is the bed from the door? 1 2 3 4 5 Okay? So it's 5 feet away.

[00:25:20]Now see what happens, basically as soon as someone starts walking, he thinks that approximately his one step will be equal to one foot, so he will take five steps and reach the bed. Did you understand? In this way he gets a lot of benefit from this map. Is this clear? So as we can see a lot of questions from this, similarly now you have think and reflect questions, let's start with that. So what is the first think and reflect question? So now related to this you have think and reflect. What are you saying in Think and Reflect? What are the standard widths for a room door? Look Around Your Home and in School. Look around your school and your home to see what is the standard width of the door of your room. How wide is that? Ok? So normally the average height is up to 3 feet.

[00:26:14]Ok? It is 3 feet tall. So if someone is older it could be 3.5. It depends on how big a door you need. But if we talk about the standard, then the standard remains standard or you can tell the average width of the door. The average width of a door, whether it is in your home or in your school, is up to 3 feet.

[00:26:44]Ok? Similarly, look around your home and in school, you can see it around you. So it can be more than this, it can be less than this. The rest depends on the need. According to what the room is like, it depends on the rooms. And if we talk about schools, there are some bigger ones in the schools.

[00:27:04]Ok? So this is it for the house. If we talk about school, it can be a little wider than 3 feet because a lot of children come there, so two queues are made, sometimes two queues are entering, so inside the school you can write, in these schools it should be a little wider, in these schools it should be a little more wider than 3 feet, okay, next question is are the doors in your school suitable for the people in wheelchairs? If any person is there, either a teacher or a student or someone's parents are coming or any person who is on a wheelchair. Ok? So are the doors of those rooms suitable for wheelchairs? So it is obvious that the wider the wheelchair, the better it will be.

[00:28:02]Ok? The wider it is, it does not mean that you cannot enter any room. So the doors of the rooms should be made in this manner only.

[00:28:13]Be it home, be it school, be it anything. So that the wheelchair inside can go inside. So it is the same inside our school. If you look around in your school, you will notice how wide the doors are.

[00:28:28]Right? So yes. So you can mention yes further.

[00:28:31]School doors should be suitable for the people in wheelchairs. So wider doors help wheelchair users to move more comfortably and safely without difficulty.

[00:28:44]Right? So yes, even inside our school the doors are wide enough to fit such suitable wheelchairs.

[00:28:49]Ok? So this was its first think and reflect.

[00:28:55]Next you have Think and Reflect.

[00:28:57]Next you have what is the x coordinate of a point on the y axis. So let me clarify it to you once again that as we read, this is your x axis. It is positive here. Here comes the negative x axis.

[00:29:13]Your positive y axis goes up and your negative y axis goes down. We also call this whole thing a Cartesian plane.

[00:29:23]Also called Cartesian plane. Ok? We also speak of coordinate systems.

[00:29:31]Is the coordinate correct? And we also call it xy plane.

[00:29:34]So there are so many names. xy coordinate plane, Cartesian plane. So these are all its names. Ok? Now what do coordinates mean? Like we discussed earlier, like here it is 1 2 3 4 5, here -1 -2 -3 -4 -5 so 1 2 3 4 will continue. Similarly, here -1 -2 -3 -4 will continue like this. Ok? Now here, as I told you, there is any point, let's say this is this point here randomly.

[00:30:07]Suppose there is this point.

[00:30:09]What are the coordinates of this point? So what do you mean by coordinates?

[00:30:13]What is the value of x y here? So if I notice, if I take it down, three is coming down and four is coming towards this side.

[00:30:22]Ok? 3 and 4. How do you write? First we write down the value of x x. Then we write the value of y. So this is point a. So the coordinates of a are you have 3 and 4. Now what is the question here? What is the x coordinate of a point on the y-axis? is any point on the y axis.

[00:30:43]Suppose this is the point. Ok? is on the y axis.

[00:30:46]What coordinates will be formed for x in it?

[00:30:49]Now look what was here? This point was randomly on any one plane. Isn't it?

[00:30:54]So the x coordinate here was your three. The y coordinate was your four. Now it is here.

[00:31:00]Look what happens here. Your origin is in this center.

[00:31:03]This is called 0. So this is the y axis. If we talk about y, what will be its x? x This will be the x axis.

[00:31:11]So on the x axis, this is 0. So this is what are the 0 and y coordinates? Two.

[00:31:17]Ok? If this point was here then it would have been 1 2 if it was here then it would have been 2. Ok?

[00:31:22]But here it is. Here it is 0 and 2 and if it had happened here then it would have been -1 and 2. So that means what are the x coordinates on the y axis? 0 Whether you take this point.

[00:31:38]What will be the coordinates of this point?

[00:31:40]0 -3 What will come of this? 0 4 What will come of this? 0 -1 What will come of this? 0 Both are 0 at this point.

[00:31:50]Ok? So if we talk about x coordinates, x coordinates on the y axis, what are those? Zero. Similarly, if I say, if I am writing extra here.

[00:32:06]Ok? If I say y coordinates y coordinates is probably next as well. No, it is not next. That's it.

[00:32:15]y coordinates on the x axis.

[00:32:18]What are the y coordinates on the x axis?

[00:32:20]This is your x-axis. Pick any point above this.

[00:32:23]This is the point. What will this point be? First you will write the value of x. - What is 3 and y? So you will see it from here, right?

[00:32:31]what is y? y is zero. So the y coordinates on the x axis are zero. So pick this up. What will happen to this? 5 0 Take this 2 0 - 4 0 So what are the y coordinates on the x-axis? There are zeros. Is this clear? Ok? Next comes the question to you. Is there a similar generalization for a point on the x axis? Is there a general generalization of a point on the x axis? The same thing comes up that I just told you about on the x axis, right?

[00:33:11]What are the y coordinates on the x axis always? There are zeros.

[00:33:13]So this is our similar generalization. That means it is exactly similar to this. Like the x coordinates are zero on the y axis.

[00:33:24]Ok? 0 y will come. y means it can be any value here. Similarly, the y coordinates on the x axis will always be zero.

[00:33:33]So x will always have some value and the y coordinates will always be zero. So you can mention here, yes.

[00:33:41]y coordinates This is generalization, that is, which is applicable to everyone. The y coordinates on the x axis is zero. Ok? So this was his second question. Next question.

[00:33:55]What is Question Third saying? Does the point q y x ever consider with the point p x y Justify your answer. So what I am saying is whether it will ever happen that a point where y x is written is considered different from a point where x y is written. Didn't you understand the meaning? Look at this thing, understand what they are saying. Let P be a point.

[00:34:26]Ok? Its coordinates are X Y. X Y and any one point Q. Its coordinates are Y X. Now let's say the value of X is two and the value of Y is three. So what are the points of P now? What happened to the points of 2 3 and Q? 3 2. What will happen if I take it on a plane? 1 2 3 1 2 3 Now look, locate the P coordinates. P is two and three, meaning X pays two and Y pays three. X pays to Y at three. here comes the. This is 2 3 So this is your P point.

[00:35:05]Ok? Let's talk about Q. Q is saying 3 2, that is, X pay three and Y pay two, that is, X pay 3 Y pay two, this point will come. This is Q means 3 2. Now these are two different points.

[00:35:18]He is saying that will it ever happen that if we have written 2 3 and it gets changed back or forth then will we ever consider it. Consider means that we will come to the same point. So yes, you can come.

[00:35:30]If both of these are same. See, if I write any value here, I write 1 2.

[00:35:37]So what will be the value of q? There will be 2 1 different points. If I write 5 6 for p, what will happen to q? 65 So these will also be separated. But if I write this, I write any, I write too too. Now if we move this forward or backward, what will be the value of q? Two two. So what will be the points of both of them now? The beans will come. Did you understand this? So here we can write yes it is possible only if x = y. What does x = y mean? Whatever is written here should be written here. So that when we reverse it, it comes here. Either 1 1 3 33 3 so in this way only and only if x = y then this thing is possible for you. Ok?

[00:36:26]Next, if x = y is not true, then we know that x y is not equal to y x.

[00:36:33]Like I just took the example. Suppose both are not equal. That means 2 is not equal to 3, so that means 2 3 is not equal, 3 2 had different points. We just saw it.

[00:36:44]Ok? And these two are equal if and only if x = y is this claim true? Yes. This is what I have just explained to you at this point. This is what I told you that if these two are not equal then the points that we write will come out different. These points will come to you only if both are equal. That means 2 2 only then 2 2 = 2 2. If we assume there is four here then 4 = 4 4 = 4. So yes, we will mention this only. Yes This Is True That If x = y means that x = y. Also, if these two are equal, it means what will these points be? Will be equal.

[00:37:40]So you will have to write both these things if both these points are same. Ok? You should notice this thing here also.

[00:37:48]Let's say this is a point 2. Ok? So 2 = 2 is equal only if these two are equal. x = y are two to two.

[00:38:05]If these two are equal then what are these two points coming from? The beans are coming.

[00:38:08]So you have written it in both these ways.

[00:38:10]Is this clear? So these were its think and reflect. So thank you. That's all for this video. In the next video we will cover exercise set 1.1. Thank you.