Translate four units right and one unit down, then reflect across the x-axis. All right, let's translate it first. Let's write out our points and then reflect it and write out our points again. I'm supposed to go four to the right and one unit down, so let's go one point at a time. Let's start with F.
F is going to be one, two, three, four to the right. one unit down F prime. Go to the next point in no particular order.
G is going to be one, two, three, four to the right, one unit down, call it G prime. And Y has me going one, two, three, four to the right, one unit down Y prime. Let's list out those points.
F prime. Starting from the origin, the way I get to f prime is I go left 1 up 1, 2, 3. So left 1 is negative 1. Up 3 is positive 3. Okay. G prime has me starting at the origin, not moving left or right.
So that's 0. And having me move up 1. So 0, negative 1 is g prime. Y prime, let me make that dot a little bit bigger. You'll see why in a minute.
is I start at the origin, go left one, don't move up or down. So Y prime is going to be left one, don't move up or down. So this is my first image.
This is my first transformation. Okay, bada bing. My second transformation now has me reflecting it across the X axis.
So I'm going to draw my mirror. That's why I made that that big. I'm going to draw my mirror across the x-axis.
Now when you reflect an image, you take a point, find out how far away it is from the mirror, and write it out that many units away on the other side. So if I take g prime, for example, and notice that g prime is one unit away from the mirror, I'm going to write out its image one unit away. I'm going to call this g double prime because it's my second image. F prime is one, two, three units away. One, two, three units away is F prime.
Y prime is living on the mirror, which means Y prime and Y double prime are exactly the same. Connect the dots. Connect the dots. And you can see we have a reflection.
So let's write those points out. F double prime, just to stay consistent. If I start at the origin, F double prime appears to be left 1 down 1, 2, 3. So left 1 is negative 1, down 1, 2, 3 is negative 3. G double prime appears to me, I don't move, but go down 1. So 0, negative 1. F double prime has me going, I already did F double prime.
Y double prime has me going left 1, don't move. So negative 1, 0. As you can see, when I reflect over one of the axes, not much changes except for the Y value in this case is now negative. Or the opposite, I guess I should say.
It's just a fun little shortcut if you memorize. stuff. But this is me doing two transformations in one coordinate plane. Awesome.