 Section 13.5 deals with coordinates in space, not just in a plane, but in space. You're going to want to take some quality notes, so pull out your notebook, slide this into your table of contents, and let's get going. Finding the coordinates of this point, basically it's just finding the x-coordinate and then finding the y-coordinate. However, this point is actually a point in space. And so instead of merely an x and a y-coordinate, we actually have a height as well, we have a z-coordinate to deal with. And so when graphing coordinates in space, it requires a little bit of extra work. So that's what this section is all about, locating points, not on a plane, but points in space. So this 3D graph grid, the x-coordinate is kind of the front-back direction. The positive is front or forward, sort of towards you, and backwards is the negative x-direction. The y-coordinates are the left and right direction. Positive is right, negative is left. And then z refers to the up and down direction, so z positive is up and negative is down. So let's graph some points using this information. So first example here, we want to plot the point 384. So first, let's take a look at that 3. So 3 refers to the x-coordinate, and since it's positive, we're moving 3 forward. In other words, towards you if you're to kind of look at this in perspective. So there's 3. Next I see 8, and 8 refers to the y-direction. So we're going to move right 8 units. And now we're kind of going to make a netting. So we're going to create a parallelogram using these two sides. Again, the red is 8 units in the right direction. The blue is 3 units, kind of in the forward direction. And then next, take a look at the y-coordinate. So, not the y, the z-coordinate. So the z-coordinate is the up and down direction. And since this is a positive z, we're going to move 4 units up. Now, the trick is, at each of the vertices of the original parallelogram, the blue and the red, I'm going to move up 4 units. And so we're kind of creating a rectangular prism, right? This netting, which has dimensions of 3, 8, and 4. Now one of the vertices, one of the corners of this box, is the point 384. And so we'll move in order. Start with the x, we'll move 3 units forward. We'll move 8 units to the right. And we'll move 4 units up. And so that corner is the point 384. Let's try another example. So in number 2 here, it says plot 6, negative 4, 2. So 6 refers to the x direction. Since it's positive, we're moving 6 units forward. Next, we have a negative 4 for the y-coordinate. And that means we're moving 4 units in the left direction. After you've plotted the x and y points, I'd like you to make that rectangle, not the rectangle, make that parallelogram that represents 6 units forward and 4 units to the left. Now at each vertex of that parallelogram, you're going to move 2 units in the positive, in other words, the up direction. And then if you connect the dots, we have ourselves our netting, which is 6 by 4 by 2. And then our job is to plot the point 6, so 6 in the positive direction for x. 6 is forward 6 to the left 4. And up 2. And so our point is that vertex. It's that corner of the pyramid, of the prism. So that's how to graph 3-dimensional points. You'll get a bunch of practice in class. But two last things. If you recall the distance formula, when we just had x and y points, this was the distance formula. When we add a z-coordinate, the distance formula gets a little bit longer. But it makes sense. We're just adding in some extra coordinate information. And likewise, the midpoint formula. Midpoint formula was x1 plus x2 divided by 2, y1 plus y2 divided by 2. If we talk about midpoint formula in space, then all we do is add in a component for the z-coordinate. And there we go.