 Welcome friends to another session on Coordinated Geometry, so in the other video we saw how Coordinated Geometry got evolved, how it got associated with mathematics, we also saw white application areas of Coordinated Geometry, so including GPS, including graphics, visual effects, entertainment, gaming and manufacturing. You name it and Coordinated Geometry is involved over there, so in fact in geography also if you see you would have studied about latitudes, longitudes, all that is it, so equator is at zero degree and things like that, so basically all of this is linked to Coordinated Geometry. Now in other subjects as well, for example in vector algebra or let's say in complex numbers later on when you will be taking up higher mathematics, there also you will see the knowledge of Coordinated Geometry becomes very very handy and it comes so useful, right, so hence it is pertinent for us all to study Coordinated Geometry and understand what it means, how it is useful in mathematics and what are the different aspects of Coordinated Geometry. So let's begin, in this session what we are going to do is we are going to define the basics of Coordinated Geometry, so what all terms are there so that you know next sessions when we are discussing about those things it becomes clear to all of you, okay, so you can see I have shown here a white sheet, graph paper like sheet, right, so in your previous grades you would have used a graph paper and the graph paper is nothing but a grid like structure or sheet of paper which is divided into so many parallel lines or cut by so many parallel lines and then there are lots of squares in it, isn't it, so this is what it looks like, so this is just a typical graph paper this thing and on top of it we are also showing two lines and what do you observe guys, so if you see these two lines are mutually perpendicular to each other, this is what the observation is, so imagine your table on which your laptop is kept right now or a sheet of paper on which you write anything, so you can imagine that paper is there and in that paper what you have done is you have just taken two mutually perpendicular lines, you need not be exactly at the center anywhere, you just draw two lines which are mutually perpendicular, now the question is can it or is it necessary only to be having a perpendicular line, can I not draw a line like this maybe, so let's say I'm drawing a line like this, let me draw a line like this, so can't I have a line like this, is it not possible, why can't I have another line drawn like that, so we'll discuss that as well, before that we have to just tell you what exactly these things are, so hence what I'm saying is any given plane, so the word is plane, so this word is what we are going to talk about, so any plane, so plane can be sheet of paper isn't it, so this is a plane sheet of paper, your ceiling, your floor, walls of your room, cover of your book, table top, bed sheet cover, anything carpet all these are plane, screen, computer screen right now on which you are seeing it or maybe a mobile phone screen, all are examples of plane, so when there's a plane and not that aero plane, so that is also called plane in short but this is a plane which is you know a flat surface, okay, now in any flat surface or a plane I can always draw these two perpendicular lines anywhere, so you know they need not be in the center or the corner anywhere, once you do it then it becomes very easy to locate any other point on that plane, what do I mean, so let me just give you an example, so let's say here is a point or you know better would be, let's say this is your home, this particular point is your home, just an example, okay or you can imagine there is a google map or a map, simple map and there are two cities A and B, B is the you know your reference point from where let's say there is another city C, okay, so what you're doing is if you have to reach A what you're doing is you are going from B to C like that and from C to A, okay, so you'll reach A if you go like that, now you'll ask why do I need to go like that, you can go in any random direction you will be reaching A for example you can say that I can go like this, right, you can go like that, yes you can definitely, but let's say don't you think this is also one of the several ways of going it, going towards A, now why this is important is, so if you now see this point A can be uniquely defined, defined in the sense where is this point A on this plane or let's say this was your home, B is your home and A is your school, let's say you are in your school, so with reference to the home the school can be uniquely defined how, so I can have this that okay there is a point C here, so which is let's say U distance away in this given it is given as U but I'm saying let's say X, so you walk or cycle down or take a car or bus X kilometers to C then you take a left turn and go to A for Y kilometers, so hence this point A is X towards let's say this direction is east and then after covering X kilometers towards east you take a left turn and move towards north and you reach A correct, so hence if I denote this X by A by XY this these two numbers X and Y let me take an example let's say this is 10 or in this case anyways I have the numbers with me, so you can see C is four kilometers let's say this one unit is one kilometer, so C is four kilometers away from B in the east direction and from C A is three kilometers away is it okay, so can I not say I can denote this A by this new method what is this, so I'm writing the X value that is four and three later like that, so four and three will denote that you have to come four kilometers towards east then take a left turn and go to go towards A three kilometers right, so hence you will reach A, similarly you could have done this way as well, so you could have gone to this point first three kilometers and then you could have gone to A like that, you reached your school through these two methods these two paths and the uniqueness about this path is it is very regular shaped, so you can see there's a 90 degree here, so only 90 degrees are allowed if at all let's say and only one turn is allowed, so then you can go like this okay, so four comma three becomes the this is called the coordinate or it's like the pin number of your school coordinate four comma three is coordinates of A okay, this is what we say coordinates of A okay, so why is this unique because if you take any two other values for example let's take random values X is equal to seven and Y is equal to five let's say, so where will I reach, so here is you have to go seven units here and then you have to go up five units is it it, so like this like that the previous case, so this point here is seven this can be written by seven comma five okay, what do we observe from this fault, so we see that any point in the plane let's say this is the point, so what is this, so if you see if I have to reach this point let's say D, so how do I go, so first in X you know in west direction I'm going, so let's say this is west direction west, how much distance did I cover five and from here I went up to how many kilometers, so one two three four five this is also five, so five, so how do I represent D shall I write five comma five if I write five comma five then I will not be able to differentiate this five comma five with let's say this number, this is also five units, the only difference is this is in east and this is in west is it it, this is in east and this is in west, so how do I differentiate between these two, so I just put a point negative sign here because if you would consider this to be positive, east to be positive you can easily see west to be negative right, so you can see the numbers are also like that, so this this differentiates point D with point let's say E, though they're the distances are same but they are in the east direction one is in the west direction, so hence the negative sign will help, so what where will be minus five comma minus five, so if you see minus five comma minus five will be somewhere here, so minus five in this direction and then minus five in the south, okay so this point is minus five comma minus five and what about another one let's say minus five uh five comma minus five so if you see five comma minus five is this, so we see that any point on this graph paper can be uniquely when I say uniquely meaning there is only one way of doing it, so uniquely by pair of numbers which are also called ordered pair, ordered pair, why ordered pair because in which order they are written is very very important, can you see five comma minus five is at this location the pin number is totally different but minus five comma five is totally opposite direction here, so that means in which order you are writing the numbers are also important, so if you change the order you'll get to some other location, so it's like if the orders are changed then instead of America and GPS you'll be appearing to be present in let's say Brazil or somewhere else, so that's how ordered pair works or meaning thereby we can define, so we can define any point for that matter any point you take this point this point and this point you will always get two numbers or even if they are not integer values let's say here randomly placed anywhere anywhere here here and all that all of this will give you some unique combination or pair of numbers for example if you take this one what is this this is seven comma minus two y seven because it is x in x it is seven and down here minus two like that I hope you understood what is meant by you know coordinates how a point can be defined in any given plane in terms of two numbers which are called ordered pair and this is what is the first learning of the day, so apart from that let us also define some things or name them, so for example this is called we don't talk in terms of east and west and all that this is called x axis x axis so this is denoted by x let me change another color and this is x dash x x dash is east west line you can say like that and this is y and this is called y y dash okay and any for example this was seven comma five right or this is seven comma minus two so this number the first number of this pair is called x coordinate x coordinate or it is also called apsica or apsisa whichever way you want to pronounce it apsica or apsisa and this one is coordinate coordinate or it is also called y coordinate i'm writing in short y coordinate okay so this is the x coordinate this is the y coordinate okay here also this is x coordinate and here it is y coordinate isn't it here this is x so first x and then y okay now questions could be is it the only way of doing it can we have a third coordinate as well yes in 3d geometry if you see there will be other lines we imagine a line from b coming towards yourself perpendicular to the screen of you know your phone or a tablet or a pc wherever you are watching it so play a line which is coming from b towards you okay so that becomes the z coordinate and imagine any point just above the screen or behind the screen so you can define that using the third coordinate as well right so we will take that up in a 3d geometry course but right now we are going to confine all the discussions on a 2d plane so i hope you understood what are the coordinate axis what is x coordinate of a point what is y coordinate of a point and what is physical significance of x coordinate and y coordinate so x coordinate is nothing but if you see here the point x y a is x y so x coordinate is nothing but distance of that point from y axis this is called x and what is y y is nothing but distance from the x axis right so this is this distance is y this distance is y okay for any x and y for example in this case if you have seven comma minus two so seven is distance from y axis that is the x coordinate so please mind the order in which i am saying seven is the x coordinate which is distance from y axis minus two is the y coordinate which is distance from x axis and minus and plus denotes whether it is on the positive side or on the negative side other information is if you see the entire sheet is let me just turn it off so entire sheet is divided into four parts right so the moment you draw two perpendicular lines you divide the entire sheet into four parts so this part here where both x and y are positive if you see all the if now i take a point here a let's say another point here and show you its coordinate okay so if i show you its coordinate right c seven comma four both are positive both are positive so this is called first quadrant guys if i take this here see minus five comma four the x coordinate becomes negative it is called second coordinate or second quadrant then see how different at different different locations the values of x and y are changing right here see minus five comma minus two so minus five minus five comma minus two this is third quadrant and here six comma minus three fourth quadrant y is negative is it x is positive here x is negative y is positive okay here both x and y are negative here both x and y are positive so you can just play around with this point and understand see different different locations both positive here only x is x is negative here both are negative here only y is negative like that so first quadrant second third and fourth so this is what is the basic information before we jump on to different concepts in coordinate geometry so i hope you understood the meaning of the terms let's again meet in the next session and understand different concepts related to coordinate geometry thank you guys for your time see you again bye