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

Example identifying the center of dilation


2m read
·Nov 11, 2024

We are told the triangle N prime is the image of triangle N under a dilation. So this is N prime in this red color, and then N is the original; N is in this blue color. What is the center of dilation? And they give us some choices here: choice A, B, C, or D is the center of dilation.

So pause this video and see if you can figure it out on your own. There are a couple of ways to think about it. One way I like to just first think about what is the scale factor here.

So in our original N, we have this side here; it has a length of two. Once we dilated it by and used that scale factor, that corresponding side has a length of four. So we went from two to four. We can figure out our scale factor: the scale factor is equal to two. Two times two is equal to four.

Now, what about our center of dilation? One way to think about it is to pick two corresponding points. Let's say we were to pick this point and this point. The image, the corresponding point on N prime, is going to be the scale factor as far away from our center of dilation as the original point.

In this example, we know the scale factor is 2, so this is going to be twice as far from our center of dilation as the corresponding point. Well, you can immediately see it’s going to be in the same direction. So actually, if you just draw a line connecting these two, there’s only one choice that sits on that line, and that is choice D right over here as being the center of dilation.

You can also verify that. Notice this first point on the original triangle: its change in x is 2, and its change in y is 3. To go from point D to point 2, that point, and then if you want to go from point D to its image, well now you’ve got to go twice as far. Your change in x is 4, and your change in y is 6.

You could use the Pythagorean theorem to calculate this distance and then the longer distance. But what you see is that the corresponding point is now twice as far from your center of dilation.

So there are a couple of ways to think about it. One, if you connect corresponding points, your center of dilation is going to be on a line that connects those two points, and that the image should be the scale factor as far away from the center of dilation. In this case, it should be twice as far from the center of dilation as the point that it is the image of.

More Articles

View All
Homeroom with Sal & Dan Roth - Wednesday, November 11
Hi everyone! Welcome to the homeroom live stream. Sal here from Khan Academy. I’m excited about our conversation today with Dan Roth, editor-in-chief of LinkedIn. A lot to talk about on both the future of work and a lot on just the future of media too. I …
Divided government and gridlock in the United States | Khan Academy
We have this diagram here, party divisions of the United States Congress. What this helps us visualize is which parties controlled the various houses of Congress, as well as which party was in control of the White House. For example, during Lyndon Johnson…
Elon Musk Giving 1,000,000 Every Day Until Election!
Uh, we are going to be awarding a million every day from now until the election. The world’s richest man just chucking millions of dollars at people to register to vote. What did you think? Well, again, for full transparency and disclosure, my son works …
Perfect Aspect | The parts of speech | Grammar | Khan Academy
Hello Garans. Today I want to talk to you about the idea of the perfect aspect of verbs. What that means is that it’s not, you know, beyond reproach or that it’s like beautiful and shiny. No, no, no. What it means is really that whatever we’re talking abo…
Get to Know the Gorillas of Disney's Animal Kingdom | Magic of Disney's Animal Kingdom
On the Gorilla Falls Exploration Trail lives a very special resident. This is our family troupe of gorillas. They’re a big group; all of our kids were born here. So we have Lily, she’s our oldest. She’s 12. There she is. Lily is probably my favorite. She…
LC natural response example
So, in previous videos, we worked out an expression for the current ( i ) in an LC circuit like this, and what we found was that ( i ) is the square root of capacitance over inductance times the starting voltage ( v_0 ) times sine ( \omega_0 t ). And ( \…