 In this video, we are looking at what are called translations. So we just finished talking about reflections are a flip over a line, usually. Well, a translation is what we consider a slide. And what you do is each point is going to slide either left, right, up, or down. Or it could go left and down, or right and up, or right and down. Any combination of those. So if you think about a really rough sketch here, if this is my coordinate plane, and I put just a simple triangle, let's say, right here. When I do a translation of that triangle, what happens is my three ordered pairs, these three vertices, are going to just slide in any given direction. So for example, if I say that the translation is x plus 2 and y minus 5, that means that I am moving all of the x values two units to the right, and it means that I'm moving all of the y values five units down. So if you think about shifting to the right, which is this way, and then down, what's going to happen is that your result, and again, this is just a rough sketch, but if I just pretend that I'm going two units over and five units down, let's say that my triangle then ends up here. So I'm shifting to the right two and down five. To the right two and down five, to the right two and down five. So your translation is just a slide. This example is going to give you a better idea of what a translation looks like. So what we have are four ordered pairs, h, j, k, and l, and we are going to translate, so we're going to shift these four points to the left three units and five units down. Well, what that means is that the rule is all of the x values are going to be shifted to the left three. Well, that means subtract three, and all of the y values are going to be shifted down, so that's going to be y minus five. So first thing I'm going to do is put h, j, k, and l on my graph. So go ahead and take a second and do that on your own. Okay, so I have h, j, k, l on my graph, and you can see that it appears to be probably a parallelogram, but definitely a quadrilateral of four sided shape. And what we're going to do is we're going to take each of these points and we're going to shift them to the left and down. So using our rule that we came up with over here, if the point h is at one zero, if I take that x value of one and subtract three, one minus three is negative two, and if I take that y value of zero and do zero minus five, I get negative five. So what that means is that the image of h is at negative two, negative five, and that would be this point right down here. So that's h prime. And if you count on your graph, you can see one, two, three units to the left, one, two, three, four, five units down. So all we've done is slid h to the left and down. Go ahead and complete the rest of these three points, j prime, k prime, and l prime. So hopefully this is the result that you got. Zero four is now at negative three, negative one, so we've shifted to the left three and down five. k, the point two five, is now at negative one zero, so to the left three and down five. And the same thing with l. We've gone to the left three and down five. So this is a translation. All we've done is taken this quadrilateral and slid it to the left and down. In this example, we are working backwards. We're given an image and we want to find the translation. So describe the translation of RECT to R prime, E prime, C prime, T prime. So all you're going to do is figure out how are you getting this point R from this point that it's at to its new location. And if you just count, you can see that it's going to the left, I'm sorry, to the right two and down one. So what we would say is that all the x values are being shifted to the right two. So that's adding two and all the y values are going down one. So that is y minus one. And then you can double check and make sure that that follows for all of the different points. For example, if I say E is at the point negative two, positive two, and I apply this rule, negative two plus two should be zero and two minus one should be at one. And sure enough, we see that that point is at zero one. So all that is happening here is these points, this rectangle, is being shifted or slid to the right two and down one.