 In this video, I'm going to talk about translating points. We're going to talk about translating points by moving them horizontally. Now, there's a couple of different ways we can move them. We can move these points either horizontally or we can move them vertically. I'm going to start with horizontally and then on my next slide, I'm going to talk about moving them vertically. Okay, so we're going to start with this point. We have this point which is negative 3-2 right here. And so what I want to do is I want to translate the point four units to the right. So we have a picture here to help us with that. So I'm going to take this point and move it one, two, three, four units to the right. Four units to the right. So now my point is right here, nice and big. Okay, so now what are the coordinates of this new point? One, one, two. So those coordinates are one, two. Okay, so notice how the coordinates change. We went from negative 3-2 and now we have a new coordinate of one, two. And as I look at that, it looks like the X coordinate changed. But notice the Y coordinate. The two there, that didn't change. The Y coordinate didn't change. Okay, so now let's look at this more using some notation. So I used to have the point negative 3-2. And now what I'm going to do is I'm going to change that point. I'm going to take that negative 3. Now notice only the negative 3 changed into a one. Now how did it change from negative 3 to 1? Okay, well notice that we're moving four units to the right. So we're actually going to add four. You can think of this as a number line. If I go to the right four, that means I'm adding four. Okay, and then the Y coordinate didn't change. And so now we're going to have a new coordinate of one, two. Okay, so we can kind of see here we started with this point negative 3-2 and it got changed by adding four to the X coordinate. And now my new coordinate is one, two. Okay, so that's one way to look at it. Okay, so you have a picture to look at it. More moving four units to the right. We have this notation here of looking at it. So in general, if I want to move a point left or right, if I want to take an XY coordinate and I want to move it horizontally, if I want to move it left or right, what I want to do is I want to take the X coordinate and I'm going to add or subtract some number. We'll call that number H. Okay, so we're talking about in general, so we're going to use a lot of variables here. So I want to take that X coordinate and I want to add or subtract some number to it, but I'm going to leave the Y coordinate alone. Okay, so if I want to take a coordinate, if I want to take a XY coordinate, if I want to change it horizontally, I'm going to add or subtract to the X coordinate. It depends if I move left or right. If I want to subtract, I'm going to move it left. If I want to add, I'm going to move it right. That's one way to look at it. Okay, or you can also think H is a positive number. I'm going to move right. If H is a negative number, I'm going to move left. That's one other way to look at it. Okay, so that is moving. That's translating points horizontally very quickly going over that. What about translating points moving vertically? Okay, so this is very, very similar, but just a little bit different. So kind of the same, we have the same point here, so we want to translate the point three units down and we're going to move this around just a bit. What we're going to do is we're going to translate this point three units down and see how the coordinates are going to change. We're going to see how these coordinates change. Okay, so start here with this point and we're going to move three units down. One, two, three. So we're moving down, we're moving down three units. So there's my new point right there. Okay, now what are the coordinates of this new point? Okay, one, two, three, so that's a negative three, one. So negative three, one are the coordinates of my new point. Now, just like last time, we're going to look at these coordinates. Notice that the X coordinates didn't change, but the Y coordinate did change. Oh, I made a mistake here. It's supposed to be a negative one, my mistake. So we went from negative three to negative three. The X coordinate didn't change, but the Y coordinate here, two and negative one, that looks like it did change. It looks like it did change. Okay, so let's use a little bit of notation to see how that changed. So negative three, two, it changed. I translated it. Now, the negative three, the X coordinate, it just stayed the same, but the Y coordinate, we took this two. Now, as you can well imagine, if we go down three, if the point is going down three units, we go from two to negative one. If I want to go down three units, that means I'm going to subtract three from the Y coordinate. I'm going to take this two, this Y coordinate, and I'm going to subtract three from it. That's moving down three, and that's going to change that point to negative three, negative one. This point is the same as what we have over here in the picture. Okay, so again, this is using the notation to kind of figure out what the new point is going to be. So in general, if I want to move vertically, if I want to move vertically, I'm going to take my X, Y coordinates, and what I'm going to do with them is I'm going to leave the X alone, but I'm going to take the Y coordinate, and I'm going to add or subtract some number. Now, I used H last time. Let's use K. Why not? Let's just use some other variable. So I'm going to take the Y coordinate. I'm going to add or subtract some number. Okay, so in this case, if I add some number, I'm going to move up. If I subtract some number, I'm actually going to move down. I'm actually going to move down, just like in this example that we have here, just like this example over here. I'm going to move down. So that's kind of what this looks like in general. I take a point. I leave the X coordinate alone, but I take the Y coordinate. I'm either going to add some number to it or subtract some number to it. Okay, that is very quickly translating points, either moving them vertically or moving them horizontally.