Topic C: Rational numbers and the coordinate plane
What we're going to do in this video is, through a bunch of examples, familiarize ourselves with the x,y-coordinate plane. And first we're going to just look at some points that are already plotted and figure out their coordinates. Then we're going to look at some coordinates and figure out where those points are. Then we'll do one more problem. So let's figure out what are the coordinates of these points? So you have this point right here, A. So its x-coordinate, you can see it right there. You just drop down. Where does it intersect the x-axis? x is equal to 5. So it's the point 5 comma and y is going to be equal to 6. 5 comma 6. Now this point B here, what's the x-coordinate? It is 5 to the left. 5 to the left of the x-axis. This is negative 5. Its x-coordinate is negative 5. y-coordinate is, if you just go straight to the right, you're going to hit y is equal to 5. y is equal 5. Let me switch colors. C. I think you're getting the hang of this. Let's do the y-coordinate first. The y-coordinate is 3. You see that right there. And then the x-coordinate is negative 2. Negative 2. You always put the x-coordinate first. That's just the convention we use. D, x-coordinate negative 2. You see that right there. y-coordinate negative 2, as well. Let me get another color. E, let's do the y-coordinate. We'll figure it out first, but you always have to write it second. It's negative 4. You see that right there, the y-coordinate. The x-coordinate is 3. And then finally, F. The x-coordinate is 2. And the y-coordinate is negative 6. Hopefully that gives you a sense of at least figuring out the coordinates. Now let's go the other way. Let's start with coordinates and figure out where those points are. So you have this first one. I'll do it lowercase case a in parentheses to differentiate it from this uppercase A. So it's at 4 comma 2. x is equal to 4. y is equal to 2. So that's that point right there. Let's do the next one. Let me do it in a color that you'll be able to read. b. x is equal to negative 3. y is equal to 5.5. So you go all the way up to 5.5. y is equal to 5.5. So that is the point lowercase b with parentheses around it. Then c, 4 negative 4. x is equal to 4. y is equal to negative 4. Right over there. And then one last one. I'll do it in orange. d, x is negative 2, y is negative 3. Right there. That's the d with parentheses. And you could have gone the other way. You could have said, hey, y is equal to negative 3. x is equal to negative 2. So you could go to the left and down. Or you could go down and to the left. And you're still going to get to the same point. So hopefully that gives you a good sense of how to figure out coordinates. Or if you're given coordinates, how to figure out where to plot something on the x,y-coordinate plane. Now let's do a slightly more involved problem. So it says the following 3 points are 3 vertices of square A, B, C, D. Plot them on a graph. Then determine what the coordinates of the fourth point, D, would be. All right, let's plot these on a graph, as they tell us to do. All right. That'll be my y-axis. That's my y-axis. The vertical axis. That'll be my x-axis. And let me put some-- let me mark it. So that's x equals 1, 2, 3, 4. This is x is equal to negative 1, negative 2, negative 3, negative 4. That's y is equal to 1, 2, 3, 4. This is y is equal to negative 1, negative 2, negative 3, negative 4. I could write that this y equals 4. This y equals negative 4. x is equal to 4. x is equal to negative 4. And let's see. Let's plot these points. So first, we have the point A is equal to negative 4, negative 4. So we go x is negative 4. And then y is negative 4. So we drop down 4 right there. And that is our point A. Negative 4, negative 4. And just to familiarize yourself with a labeling scheme that you may or may not have seen before, is that people label these sections of the coordinate plane. They call this the first quadrant. They call this the second quadrant. They call this the third quadrant. And they call this the fourth quadrant. And these are just the Roman numerals for I, II, III, and IV, So this point is in the third quadrant. When we looked up at this stuff over here, these points are in the fourth quadrant. These are in the third, second, first. Just an interesting thing to know. Sometimes someone might ask you, what quadrant is that point in? And you just say, OK, I see. If they're both negative, they're going to be in the third quadrant. If just the y is negative, but the x is positive, you're going to be in the fourth. If they're both positive, you're in the first. If y is positive, but x is negative, you're in the second. And we'll talk a little bit about that as we plot these points. So point B, x is positive. It's 1, 2, 3. And y is negative 4. So we drop down here into the fourth quadrant. That is the point B. It's 3, negative 4. So we can already see the bottom of our rectangle that they're talking about, right there. And notice, both of these have the exact same y. They're both at the same level below the x-axis. And then what's the next point? Point C is 3 comma 3. So 3 comma 3. It's in the first quadrant. Both of its coordinates are positive. 3 comma 3. Both x and y are positive. And notice, it's on the same vertical as B. It has the same x value. They both have an x value of 3. So it's right above it. Right above it. Now we have to figure out the last point here. Well, the point is going to have to be on the same vertical as this point. It's going to have to be on the same vertical as this point, which means it's going to have the same x value as this point. So its x value is going to be negative 4. And then it's going to have to be on the same horizontal as this point. It's going to have to be on the same horizontal as that point. So it's going to have to have the same y value at the same height above the x-axis. So it's going to have to be 3. So that is our point D. Notice it's at negative 4, right above A. And it's at y is equal to 3. Right to the left of point C. And we are done.