Video Transcript: Coordinate Plane

Quadrants of the coordinate plane 

In which quadrant is the point negative 7 comma 7 located? So let's just review what a quadrant is. A quadrant are each of the four sections of the coordinate plane. And when we talk about  the sections, we're talking about the sections as divided by the coordinate axes. So this right  here is the x-axis and this up-down axis is the y-axis. And you can see it divides a coordinate  plane into four sections. We call each of these sections quadrants. This one over here, where  both the x-values and the y-values are positive, we call the first quadrant. And we use the  Roman numeral I. Then if we kind of move counterclockwise around the coordinate plane, this  quadrant where the x-values are negative and the y-values are positive, we call this the second  quadrant. I could write it. We call this the second quadrant. Then we go down here where both  the x-values are negative and the y-values are negative. We call this the third quadrant, once  again using Roman numerals. Then finally the quadrant where the x-values are positive but the  y-values are negative, we call this the fourth quadrant. So let's see which quadrant the point  negative 7 comma 7 is located. So there's two ways to think about it. You could just say, look,  we have a negative x-value. Our x-value is negative, so we're going to move to the left. So we're going to be on this side. We're going to be on this side right here of the coordinate plane. Just  by the fact that the x-value is negative, we're going to be either in the second or the third  quadrant. Now, we know that the y-value is positive. We know that the y-value is positive. So if  the x-value is negative and the y-value is positive, we're going to land someplace right over  here in the second quadrant. The other way to think about it is you could literally just plot this  point and see that it falls in the second quadrant. So let's do that. If x is negative 7. So that's  negative 1, negative 2, negative 3, negative 4, negative 5, negative 6, negative 7. Did I do that  right? 1, 2, 3 4, 5, 6, 7. So this is x is negative 7. And then we have to go up 7 because y is equal  to positive 7. So 1, 2, 3, 4, 5, 6 7. So the point negative 7 comma 7 is right over here, clearly lies  in the second quadrant. 

Points and quadrants example 

Plot 4 comma negative 1, and select the quadrant in which the point lies. So 4, the first number  in our ordered pair, that's our x-coordinate. That says how far to move in the horizontal or the  x-direction. It's a positive 4. So I'm going to go 4 to the right. And then the second coordinate  says, what do we do in the vertical direction or in the y-direction? It's a negative 1. Since it's  negative, we're going to go down. And it's a negative 1, so we're going to go down 1. So that  right over there is the point 4 comma negative 1. So I've plotted it, but now I have to select  which quadrant the point lies in. And this is just a naming convention. This is the first quadrant.  This is the second quadrant. This is the third quadrant. And this is the fourth quadrant. So the  point lies in the fourth quadrant, quadrant IV. And I guess you have to know your Roman  numerals a little bit to know that's representing quadrant IV. Let's do a couple more of these.  Plot 8 comma negative 4, and select the quadrant in which the point lies. Well, my x-coordinate is 8 so I go 8 in the positive x-direction. And then my y-coordinate is negative 4, so I go 4 down.  And this is sitting, again, in not the first, not the second, not the third, but the fourth quadrant,  in quadrant IV. Let's do one more of these. Hopefully we get a different quadrant. So we want  to plot the point negative 5 comma 5. So now my x-coordinate is negative. It's negative 5. So  I'm going to move to the left in the x-direction. So I go to negative 5. And my y-coordinate is 

positive so I go up 5, so negative 5 comma 5. And this is sitting not in the first quadrant, but the  second quadrant. And of course, this is the third and the fourth. So this is sitting in the second  quadrant. Check answer, and we got it right. 

Coordinate plane word problem examples 

Milena's town is built on a grid similar to the coordinate plane. She is riding her bicycle from her home at point negative 3, 4 to the mall at point negative 3, negative 7. Each unit on the graph  denotes one city block. Plot the two points, and find the distance between Milena's home and  the mall. So let's see, she's riding her bicycle from her home at the point negative 3, 4. So let's  plot negative 3, 4. So I'll use this point right over here. So negative 3 is our x-coordinate. So  we're going to go 3 to the left of the origin 1, 2, 3. That gets us a negative 3. And positive 4 is our y-coordinate. So we're going to go 4 above the origin. Or I should say, we're going to go 4 up.  So we went negative 3, or we went 3 to the left. That's negative 3, positive 4. Or you could say  we went positive 4, negative 3. This tells us what we do in the horizontal direction. This tells us  what we do in the vertical direction. That's where her home is. Now let's figure out where the  mall is. It's at the point negative 3, negative 7. So negative 3, we went negative 3 along the  horizontal direction and then negative 7 along the vertical direction. So we get to negative 3,  negative 7 right over there. And now we need to figure out the distance between her home and  the mall. Now, we could actually count it out, or we could just compute it. If we wanted to  count it out, it's 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 blocks. So we could type that in. And another way  to think about it is they have the exact same x-coordinate. They're both at the x-coordinate  negative 3. The only difference between these two is what is happening in the y-coordinate.  This is at a positive 4. This is at a negative 7. Positive 4, negative 7. So we're really trying to find  the distance between 4 and negative 7. So if I were to say 4 minus negative 7, we would get this  distance right over here. So we have 4 minus negative 7, which is the same thing as 4 plus 7,  which is 11. Let's do a couple more. Carlos is hanging a poster in the area shown by the red  rectangle. He is placing a nail in the center of the blue line. In the second graph, plot the point  where he places the nail. So he wants to place a nail in the center of the blue line. The blue line  is 6 units long. The center is right over here. That's 3 to the right, 3 to the left. So he wants to  put the nail at the point x equals 0, y is equal to 4. So he wants to put it at x is equal to 0, y is  equal to 4. That's this point right over here. So let's check our answer. Let's do one more. Town  A and Town B are connected by a train that has a station at the point negative 1, 3. I see that.  The train tracks are in blue. Fair enough. Which town is closer to the station along the train  route, Town A or Town B? So they're not just asking us what's the kind of crow's flight, the  distance that if you were to fly. They're saying, which town is closer to the station along the  train route? So if you were to follow the train route just like that. So the A right over here, A if  you were going along the train route, you would have to go 1, 2, 3, 4, 5, 6 in the x-direction, and  then 1, 2, 3, 4, 5 along the y-direction. So you'd have to go a total of 11. If you're going from B,  you're going 1, 2, 3, 4, 5, 6, 7, 8 9, 10, 11 along the x-direction, and then 1, 2, 3, 4, 5, 6, so 6 along  the vertical direction. So you're going to go a total 17. So it's pretty obvious that A is closer  along the tracks. Now, you could also think about it in terms of coordinates because A is at the  coordinate of negative 7, 8. And if you were to think about negative 7, 8, to get from negative 7  to negative 1 along the x-coordinate, you're going to go 6. And then to go from 8 to 3, you're 

going to go 5 more. So you could also not necessarily count it out, you can actually just think  about the coordinates. But either way, you see that town A is closer.