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

Mapping shapes example


2m read
·Nov 11, 2024

So I'm here on the Khan Academy exercise for mapping shapes, and I'm asked to map the movable quadrilateral onto quadrilateral ABCD using rigid transformations.

Here in blue, I have the movable quadrilateral, and I want to map it onto this quadrilateral in gray. We have a series of tools here: rigid transformations of translation, rotation, and reflection on the Khan Academy tool. Of course, we can undo it.

The technique I'm going to use to do this is: I'm going to first use translation to make one of the corresponding points overlap with the point that corresponds to it. So, for example, it looks like this corresponds to point C right over here. I'm going to translate.

Once I click that, I can translate this around. So I'm going to translate right over here to point C. Now let's see: to make these two overlap, I really can't do any more translation. I've made one point overlap. Do I rotate or do I reflect? Well, if I eyeball it right over here, it looks like I am doing a rotation. Let me try to make use of rotation to make this segment right over here overlap with segment CD.

So let me do a rotation now. Let's see... Yep, this is looking good. There you go; we did the rotation, and we are done. Now, let's do another example.

So here, what do we need to do? All right, I'm going to do the same technique. This seems to correspond to point C, so I'm going to translate first. I translate first, and then there's something interesting going on right over here because I've actually been able to overlap points C and A by shifting it, by translating it, I should say.

It's not clear that if I were to rotate it, then I would lose the fact that the point that corresponds to A is now sitting on top of A, and the point that corresponds to C is now sitting on top of C. It feels like a reflection, and it looks like a line that would actually contain the points A and C. If we reflect over that line, then we'll be in good shape.

So let me see: reflection. Let me move the line... see how it—oops—that's not what I wanted to do. Let me move my line. So, that is, I think, a good line of reflection. Then let me actually try to reflect. There you go; I was able to reflect over that line.

My clue that I had to reflect over the line that contained A and C is that the points A and C and their images after the transformation were all sitting on top of each other. So that was a good clue: that on a reflection, if they're both sitting on the line of reflection, they wouldn't move, so to speak. And there you have it: so this was a translation and then a reflection.

More Articles

View All
Female Founders Conference - New York
[Applause] [Applause] [Applause] [Applause] [Applause] [Music] [Applause] Okay, let’s see here. Hi, hi everyone! Good afternoon! I think we’ll get started. You’re nice and cool inside, thank goodness. I lived in New York more than 20 years ago at this poi…
Don't Suffer More Than Needed | Buddhist Philosophy on Pain and Suffering
When we think of pain and suffering, we usually think about more or less the same thing. When there’s pain, there’s suffering. And we can only be free from suffering if we eliminate pain, right? Well, even though these two experiences are interconnected,…
how to ACTUALLY CHANGE your life in 2023 (step by step guide)
We all experienced failure at some point in our lives. Maybe you didn’t get that promotion you were hoping for, or you didn’t accomplish a personal goal you set for yourself. But for some reason, when it gets closer to New Year’s, we tend to be more hopef…
Combining mixtures example
We’re told a partially filled tank holds 30 liters of gasoline with an 18% concentration of ethanol. A fuel station is selling gasoline with a 25% concentration of ethanol. What volume in liters of the fuel station gasoline would we need to add to the tan…
How to use social media to sell private jets!
Uh, we’ve had a guy walk in the door here and say, you know, I saw you guys on TikTok yesterday and I’m looking to buy this jet. I made this offer four days ago. I don’t know if it’s going to succeed, but what do you think? He showed us the offer, and we…
Homeroom with Sal & Rehema Ellis - Tuesday, December 15
Hi everyone, Sal Khan here from Khan Academy. Welcome to our homeroom live stream! We have a very exciting guest, Rohima Ellis, who is the education correspondent for the NBC Nightly News. But before we get into that, what promises to be a very exciting c…