Graphs and Coordinates - Video Tutorials & Practice Problems

Graphs & the Rectangular Coordinate System

Hey, everyone. So up until now, all the graphing and plotting that we've seen in this course has only involved one variable like X and we've always plotted it on the horizontal number line. But a lot of graphing for the rest of this course is gonna involve the relationship between two variables. So we're gonna have to plot points and also equations. And in order to do that with multiple variables, we'll need to be familiar with the rectangular coordinate system. So that's what I'm gonna, we're gonna talk about in this video. And basically what I'm gonna show you here is how we can take coordinates that are described with two numbers like four comma three. And I'm gonna show you that these are really just locations on this two dimensional grid. Um And it has to do with their X and Y value. So I'm going to show you how to plot these kinds of points. So let's get started here. The rectangular coordinate system sometimes called the Cartesian plane is really just where you have a horizontal number line and a vertical number line that are sort of together and crossing these are two perpendicular number lines that come together to form a two dimension grid instead of just a one dimensional line. So now we're going to describe locations not just as an X coordinate, but also as a Y coordinate as well. So let's get into the specifics this horizontal axis that we've been familiar with so far is called the X axis. And so you're gonna see a little X written out here along this number line and then over on the vertical axis that's gonna be the Y axis. So basically what we can do is now instead of describing just 1.1 point on this number line with one number, we can actually describe using two numbers and one for the X and one for the Y. And the way that we describe points where sometimes this are called ordered pairs is basically just a position and it's always in the form where it has a parenthesis and there's two numbers an X and A Y. So for example, there's gonna be four comma three, that's an X coordinate and A Y coordinate that's called an ordered pair. Basically, what you're gonna do here is you're gonna start from the sort of center of this diagram and you're gonna go along the X A this until you hit the four, so that you're gonna go four in the X and then you're gonna go three in the Y from there. So that's what the coordinate, four comma three means. It means you go four in the X and then three in the Y. And that's why this location of A is equal to a four comma three. All right. So that's what a point or an ordered pair is. So for this example, we're just going to be plotting out a bunch of ordered pairs on this graph. So let's keep going. Now notice how in B here, I've got a negative no inside for the X coordinate. So what does that mean? Well, in order for us to understand that we'll talk about the origin. The origin really is just the center of this diagram which we've already sort of labeled over here. And it's just the 0.0 comma zero. It's where your graph starts. And it's also basically where the X and Y axis intersect and notice what happens is it also separates positive sorry, positive and negative values. So for example, what you'll see is that the X values are positive, the Y values are positive to the right and above the origin. So X values are positive and Y values are positive to the right and above the origin and then they're negative when they're to the left or below the origin as we can see over here. All right. So how do we graph the coordinate? Negative three comma two? Well, now what this is saying is that on the Y axis, we're gonna go to negative three. So instead of going to the right? Like I did for a, I'm gonna have to go to the left negative three and then I have to get to two on the Y axis. So do I have to go up or down? Well, I have to get to positive two. So I'm gonna have to go up like this. So this is the point B and this is negative three. Comma two. All right, pretty straightforward. Let's keep doing, doing a few more examples. So here we've got negative two comma negative three. Remember this is X comma Y. So here I have to go to negative two by going to the left and then I have to go down to get to negative three. That's over here. So this is the coordinate C and this is negative two comma negative three. All right. And now we have five comma negative four. So five comma negative four is going to be positive five. So here I'm actually gonna go to the right, I'm gonna have to go to the right five and then I have to get to negative four. So I have to go down from here. So this is 123 and four. This is negative four. So this over here is the point D which is five comma negative four. All right, we've got a few more, we've got the zero comma zero but we actually have already seen that before. Zero, comma zero is really just the origin. Um So that's just the location zero, comma zero. And then finally, we've got zero comma negative three. Again, what this means is that you're gonna go zero on the X axis. So you're not really gonna go left or right and then you're gonna have to go down just from the origin until you hit to negative three. So this is the coordinate F zero comma negative three. All right. So this is a little bit sort of a, you know, cluttered here. We've got a lot of points, but hopefully, this makes sense and how to sort of graph them. The last thing I want to talk about here is that a lot of these points has sort of fallen into 24 different corners of this diagram. And these are called quadrants. Basically, what happens is that the X and Y axes divide the graph into four regions or four corners and these just get names, they're called quadrants and basically they all have numbers. Um And quadrant one is gonna stop at the, it is gonna start at the top right hand corner and then you're gonna keep going uh in an increasing number as you go counterclockwise around. So this is quadrant two, this is quadrant three and this is quadrant four. Sometimes they get Roman numerals. Um But you don't really need to know that. All right folks. So that's just an introduction into graphing in the cod and system. Thanks for watching.

Graphs and Coordinates - Example

Welcome back everyone. So in this problem, we're gonna graph these points that were given WXY and Z we're given their ordered pairs and then we're gonna identify the quadrant of each one of these points. So let's get started. Now, remember whenever you're given coordinates or ordered pairs, the two numbers, the first one corresponds to the X and the second one corresponds to the Y. So the first thing you do is walk along the X axis right or left and then you go to the Y axis up or down. So let's get started for this first point. We have one common negative two. So I have walk along the X axis to one over here. And then, because I'm going into the negative, I have to go down to negative two. And so my points W ends up being over here, let's go to the next one. X is five, comma two that means five and the X two and the Y. So you walk along the X axis to five that's over here. And now you go upwards because you're going positive and both of them are positive. So you go up to the right and up and that's gonna be two. So this is gonna be your X coordinate. So now about why, why is negative three common negative four? So now both these things are negative. So you're gonna have to go to the left until you get to three. So you're going left here and then you're gonna go down to negative four. So it's down over here. So this is the point uh why? And then last, but not least we have the Z coord in negative four comma three. So now we're gonna do is you're gonna go to the left to negative four and you're gonna have to go up now three. So one, 23 and that's gonna be your Z coordinates. All right. So this is all your coordinates just always going to be really helpful to familiarize yourself with the coordinate system and how to graph some points. So now we're just going to identify the quadrants of each one of these points over here. So what about W? So remember the quadrants go, uh you start at Q one that's quadrant one and then you go counter clockwise. Um And then it goes in increasing order. So this is quadrant two, quadrant three and quadrant four. So that means that quadrant uh sorry, the W coordinate or the W point over here is actually in Q four. So this is gonna be in quadrant four. What about X? Well, X over here we located XX is this point and this is clearly in quadrant one. That's the top right corner. Now, what about yy is in the lower left and that's quadrant three. So that's quadrant three. And then Z over here is gonna be in this coordinates. So that is gonna be the top left, which is coordinate, which is quadrant two. So hopefully got that right. Let me know if you have any questions. Thanks for watching.