Example reflecting quadrilateral over x axis

We're asked to plot the image of quadrilateral ABCD. So that's this blue quadrilateral here under a reflection across the x-axis. So that's the x-axis, and we have our little tool here on Khan Academy where we can construct a quadrilateral, and we need to construct the reflection of triangle ABCD.

So what we can do is let me scroll down a little bit so we can see the entire coordinate axis. We want to find the reflection across the x-axis. So I'm going to reflect point by point. Actually, let me just move this whole thing down here so that we can see what is going on a little bit clearer.

So let's just first reflect point. Let me move this a little bit out of the way. So let's first reflect point A. So we're going to reflect across the x-axis. A is four units above the x-axis; one, two, three, four. So its image A-prime, we could say, would be four units below the x-axis. So one, two, three, four. So let's make this right over here.

A A-prime. I'm having trouble putting the... see if I move these other characters around... okay, there you go. So this is going to be my A-prime. Now, let me try B. B is two units above the x-axis. So B-prime is going to have the same x-coordinate, but it's going to be two units below the x-axis. So let's make this our B. So this is our B right over here.

Now, let's make this our C. C right here has the x-coordinate of negative 5 and a y-coordinate of negative 4. Now C-prime would have the same x-coordinate, but instead of being four units below the x-axis, it'll be four units above the x-axis. So it would have the coordinates negative five, positive four.

So this is going to be our C here. So this goes to negative five, one, two, three, positive four. And then last but not least, D. And so let's see, D right now is at negative two, negative one. If we reflect across the x-axis, instead of being one unit below the x-axis, we'll be one unit above the x-axis, and we'll keep our x-coordinate of negative two.

And so there you have it; we have constructed the reflection of ABCD across the x-axis. And what's interesting about this example is that the original quadrilateral is on top of the x-axis. So you can kind of see this top part of the quadrilateral gets reflected below it, and this bottom part of the quadrilateral gets reflected above it. And then you can see that indeed, they do look like reflections flipped over the x-axis.