yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Example reflecting quadrilateral over x axis


2m read
·Nov 11, 2024

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.

More Articles

View All
Alex Blumberg of Gimlet Media
Maybe the best place to start is which, seemingly, was the most common question. Mm-hmm. Rowe asked it, and a couple other people on Twitter: How do you source stories? That’s a really good question, and it’s one that we are sort of working to answer more…
Andy Bromberg - Startup Investor School Day 4
There was one note that someone had that I thought was a little interesting. He pointed out that, Karl, thank you, that we haven’t really talked about taxes. I can’t imagine why we haven’t talked about taxes. Well, taxes are an interesting issue when you…
How to Stop Wasting Time on the Internet - 4 Awesome Tips
[Music] If you’re watching this video, there’s a pretty good chance that you shouldn’t be watching it and should be doing something more productive instead. But if you’ve already done your work, good for you! Either way, here are four useful strategies yo…
8 STOIC TIPS FOR SOLVING PROBLEMS WITH PEOPLE | STOICISM INSIGHTS
Have you ever felt utterly overwhelmed by the noise around you, the endless stream of opinions, expectations, and the relentless pressure of ‘keeping up’? Imagine this: ancient stoic philosophers over 2,000 years ago faced the same human emotions, struggl…
Ask me anything with Sal Khan: March 27 | Homeroom with Sal
Hi everyone! Welcome to our daily live stream. This is why we’ve almost, we’ve been doing this for a little bit over two weeks. For those of you all who are new to this, the whole point of this is Khan Academy is a not-for-profit with a mission of providi…
Finding percentages with a double number line
We’re told that Omar’s class has 28 students in it. 21 of them take the bus to school. What percentage of the students in Omar’s class take the bus to school? Pause this video and see if you can figure that out. All right, well, I’m going to try to visua…