[Music] in this video we will discuss cartesian coordinate system or the rectangular coordinate system so what will be our objectives first is we're going to describe what is a cartesian coordinate system the x-axis the y-axis quadrant and the origin next is we're going to plot the given pair of coordinates in the cartesian coordinate plane and last we will determine the quadrant given a pair of coordinates so first let's go back to the concept of the number line so the number line is called a one-dimensional coordinate system so when we say coordinate it is referring to the location so therefore a number line has only one uh location there is only one location that's why it is called one dimensional coordinate system now why do we have only one location in a number line because we can only move it to the right or to the left okay so the a number line is called one dimensional coordinate system because we only have one location we can only move it to the left or to the right now in cartesian coordinate system we already have two sets of number line perpendicular to each other so therefore we can now move it up and down okay so when we have cartesian coordinate system we can now move it up and down all right so therefore our teach our cartesian coordinate system is a two dimensional coordinate system because we now have two coordinates so what is the quotation coordinate system it is a system used for graphing number pairs or ordered pairs it is also called rectangular coordinate system or mass familiar negative cartesian plane okay so let's go back to the history of cartesian coordinate system who created or proposes this so rene descartes from 19 1596 to 1650 he is the french mathematician a philosopher and a theologian he came up with many of his philosophical and mathematical ideas during his morning meditations that's why meronshang meditations for his first philosophy so the cartesian coordinate system again consists of two number lines perpendicular to each other so let's proceed to the parts of cartesian coordinate system a horizontal line horizontally so negative and positive integers at the po horizontal line that this is what we call the x-axis all right and then this one the vertical line is what we called or refers to the y-axis at the vertical line now these two axis is what we call the coordinate axis so we will have here the point so what is the intersection of your x-axis and y-axis that is what we call the origin so the origin has a coordinates of 0 0 y because the intersection of y and x axis is 0 right so magicking all right now when x axis and y and axis intersect to each other it will form four regions and that is what we call the quadrants so uh given the illustration how many quadrants do we have so how many regions and form kapagnagi intersects the x-axis at the y-axis that's that is correct we have four so we have four quadrants labeled counterclockwise okay so this is your quadrant one quadrant two quadrant three and quadrant four so remember that your x-axis capac positive um move uh if the um number is a positive you're going to move to the right if it's negative move to the left so y axis demand if it's positive you're going to move up if it's negative move down all right so we have here the ordered pair now remember that in in an ordered pair x y so since this is x your number not indito can only be found can only be found in your x axis so number can only be found in your y-axis s this number can only be found in your x-axis well this one can only be found in your y axis now focus is x values so this is what we call the x coordinate or it is also called abscissa again your x values is what we call the x-coordinate or that is also called abscissa while you're what a y is what we call the y-coordinate or that is also called ordinate okay so y coordinate or the other term for this is ordinate another name for the y coordinate so if you will be given ordered pair this is your abscissa this is your ordinate this is your x-coordinate this is your y-coordinate so when we say coordinates that is referring to the ordered pair okay let's proceed to the signs how will you know that the given ordered pair i lies on quadrant one quadrant ii quadrant iii or quadrant iv so let's focus on quadrant one so i have here etongasi quadrant one so sabina what do you think or what are the signs of quadrant one of the numbers or the ordered pairs from quadrant one quadrant first number moditos x and this one is for y-axis if this is the region for quadrant one so on x-na i positive i positive so therefore the signs of the numbers or the ordered pairs in quadrant one is positive positive now for quadrant two so ex so this is negative and then y nathan is positive so therefore the given ordered pairs for quadrant two has a sign of negative and then positive next for quadrant three we have so exponential negative and then this is also negative so therefore the pair of uh coordinates in quadrant iii has a sign of negative negative and then for quadrant four so the ex monetizing and positive and then this parts part the y-axis is also neg is negative so therefore the pair of coordinates or the ordered pair in quadrant four is positive negative so that is the sign of the coordinates of in quadrant four all right so let's have the plotting of points how are we going to plot the points in the cartesian coordinate system or cartesian plane so let's have this one now in making your own cartesian plane do not forget to put the x and the y axis okay so let's have the first one so let us plot point a which is 3 and negative 2 remember that this is your x your x coordinate this is your y coordinate this can only be found on your x axis and this one in your y-axis all right so let us try to plot this point so point a has a coordinates of positive 3 and negative 2. so positive three means moving to the right so this x-axis net n ebik sabihin start from the origin positive all right so let's try so since this is positive trees x axis moon and focus always starts from the origin so one two three because that is positive so going to the right i o and move not then and then y coordinate nothing is negative two so y axis nothing vertical so since negative tongue value nothing going down so one two so he picks a b hand point a is here all right another way is i will give you another way of uh plotting points so another way is you can also plot the points from x and y axis so hadimbawa this is positive three ipa plus a positive and then get their intersection okay so you have uh two ways of plotting points you can move right or left and then up and down or you may get there intersection okay another so i have point b negative five so negative five since it's ix axis so the two muna time for focus starts from the origin negative five so one two three four five okay from here this is positive four your y coordinates of vertical negative since positive force are going up and i o so one two three four so therefore and point b nathan is here okay another way so again when we you when you are moving points kappa left or right up and down always starts from the origin okay and then now so let you may also try plotting this points x and y axis and then get the intersection so negative five if a platform is a negative five and then if a plot goes a positive force a y axis and then get the intersection ganon parenchy all right so let's have this one let uh point c i have positive six and positive five get the intersection that is the point letter point d negative three from x axis and then negative seven from y axis and then get the intersection that is the point point e negative six lag it is x-axis maximum followed by your y-axis and then why not then y-coordinate is negative four so get the intersection that is your point e for f we have zero so zero sha and x not in a zero and then on y naught and a negative now if you will get the intersection right so therefore on point y axis now since um x coordinate not in a zero then the point uh the point negative five lies on the negative side of your y-axis so automatic um y-axis all right another so i have point g positive seven ipa and then negative five so y axis naman so let us say negative five so intersection this is your point g and then for point h so again since our uh y coordinate is zero therefore atom negative six not n magnesium x axis all right now let us try to determine the quadrants okay now uh you may just look at their signs okay but since we have the cartesian plane we can easily determine the quadrants of the given points okay this is quadrant one quadrant two three and four all right so this is your point a so this is quadrant four your point b is squadron two hasn't your point c this is quadrant one your point d this is your point d this is quadrant three your point e is also quadrant three now what are you gonna answer if you have your point lying on the y-axis so anon gaga we not so this point lies on the negative a negative part of your y-axis negative five lies on the negative y axis so y and as a y axis if you want to be specific negative y axis okay next so your point g is quadrant iv and then this one so hindi negligence because of four regions so ebik sabihin but if you want to be specific point h lies on the negative x axis okay so now i want to go to these locations now i want to go to these places help me find their locations by finding their coordinates so i want to go to these places i want to know their coordinates so that i can go there okay so for church so this is church your first number here is your x-coordinate you can only found this number the unsaating x-axis well this part can be found on your y-axis okay so young church nathan x axis negative six so that is your x-axis or x-coordinate rather five so that is five all right next i want to go to the hospital so it usha positive 5 that is your x coordinate now your y coordinate at y coordinate that is positive one next i want to go to school so this is here's your school so focused is x-axis at the x-axis positive three on the x-axis okay if you can uh still recall the discussion on the previous slide x-axis a big sub and y-coordinate nothing is zero all right so therefore your x coordinate is negative seven and then your y coordinate is zero and then i'm going to the part here so this is your x axis so that is negative five and then your y-axis is negative two okay and then i'm going to the market where's the market here so your point again lies on the y-axis so if your point lies on the y-axis therefore your x-axis is or your x-coordinate is zero and then your y-ax y-coordinate is positive four next i want to go to salon to the salon so here's the location so focus on the x-axis so that is positive four and then your y-axis is negative six and then i want to go home because i'm tired all right so what are what is the location of my home so the origin is remember the origin is zero zero so your x coordinate and your y coordinate are both zero all right that's yourself so i want you to plot the points so you may pause the video so point a i have negative three and four so where do you think uh you're going to plot point a so negative three and negative force always starts with the x axis so that is here so negative 3 your x coordinate and then your y coordinate is positive 4 so i unsure next point b i have positive 8 and negative six that is correct we have this point so positive eight and then negative six next i have negative four and negative five that is correct negative four focus x-axis and then negative five better so the intersection is here next positive one and positive three e so this is positive one for your x-axis and then your y-coordinate is positive three okay that is correct that is your point d and then number five we have negatives 2 and 0. okay so this is your negative 2 from your x-axis so next is your y-axis okay your y-axis is 0. so where do you think you're gonna uh place your point yes like it's lying on the negative x-axis okay because your y-coordinate is already zero next uh i'll be giving the points you're gonna give the coordinates or the ordered pairs so this is point f so what is the coordinate or the ordered pairs so yes that is five and one next point g correct that is positive two negative three point h so it's lagging on the negative y axis so yes if it's lying on the y axis yours uh what x coordinate is zero so zero negative six for your point i that is correct it's negative seven positive seven and for your point j that is negative six negative two okay so i hope you got perfect congratulations let's focus to the quadrant so let us now identify the quadrants of the given points so i have here point a so what is the quadrant this is quadrant one two three four so what is the quadrant of a that is quadrant 2 for b that is quadrant 3 aqua and 4 for c that is quadrant 3 for d that is quadrant one for point e okay for point e that is the negative x axis so negligible x axis point f that is quadrant one point g that is quadrant four point h that is the on the negative y axis point i that is quadrant two and number 10 point j that is in quadrant three so i hope you still got perfect congratulations okay let us answer these questions so the intersection of the coordinate axis is called what is the intersection that is the origin with the coordinates of what is the ordered pair of the origin that is 0 0 next the vertical axis of the cartesian plane is also called the anon tawagnath indus vertical axis that is the y-axis next the pair of numbers three negative one is called this is what we call the ordered pair in the ordered pair five two two is called the anata satu that is the y coordinate or it can be called ordinate next the x coordinate is also called starts with letter a correct that is the abscissa four regions formed by the coordinate axes are called so when two axes intersect ano yunta wagnat in dunsa regions that is what we called quadrants and then to plot five negative four start at that when we are plotting points we let's start with the origin and then move five units since positive five though five units to the right and then move four units negative four so four four units up or down down okay and the last one do five one and ordered pair one five represent the same point no okay five one and one five that doesn't represent the same point but they are both lagging on the same quadrant okay thank you for watching this video i hope you learned something don't forget to like subscribe and hit the notification bell for updated ko for more video tutorials this is your guide in learning your math lessons your walmart channel you