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

Determining angle of rotation


2m read
·Nov 11, 2024

We're told that triangle A'B'C' (so that's this red triangle over here) is the image of triangle ABC (so that's this blue triangle here) under rotation about the origin. So, we're rotating about the origin here. Determine the angle of rotation.

So, like always, pause this video, see if you can figure it out.

I'm just going to think about what how did each of these points have to be rotated to go from A to A' or B to B' or from C to C'. So, let's just start with A. This is where A starts. Remember, we're rotating about the origin—that's why I'm drawing this line from the origin to A.

Where does it get rotated to? Well, it gets rotated to right over here. So, the rotation is going in the counterclockwise direction, so it's going to have a positive angle.

So, we can rule out these two right over here. The key question is, is this 30 degrees or 60 degrees? There are a bunch of ways that you could think about it. One, 60 degrees would be two-thirds of a right angle, while 30 degrees would be one-third of a right angle. A right angle would look something like this, so this looks much more like two-thirds of a right angle.

So, I'll go with 60 degrees. Another way to think about it is that 60 degrees is one-third of 180 degrees, which this also looks like right over here. If you do that with any of the points, you would see a similar thing.

So, just looking at A to A' makes me feel good that this was a 60-degree rotation. Let's do another example.

So, we are told quadrilateral A'B'C'D' (in red here) is the image of quadrilateral ABCD (in blue here) under rotation about point Q. Determine the angle of rotation.

So, once again, pause this video and see if you can figure it out. Well, I'm going to tackle this the same way. I don't have a coordinate plane here, but it's the same notion. I can take some initial point and then look at its image and think about, well, how much did I have to rotate it?

I could do B to B', although this might be a little bit too close. So, I'm going from B to (let me do a new color here just because this color is too close to...) I'll use black.

So, we're going from B to B' right over here. We are going clockwise, so it's going to be a negative rotation. So, we can rule that and that out. And it looks like a right angle. This looks like a right angle, so I feel good about picking negative 90 degrees.

We could try another point and feel good that that also meets that—negative 90 degrees. Let's say D to D'. This is where D is initially, this is where D is, and this is where D' is.

Once again, we are moving clockwise, so it's a negative rotation. This looks like a right angle—definitely more like a right angle than a 60-degree angle.

So, this would be negative 90 degrees. Definitely feel good about that.

More Articles

View All
Mike Knoop on Product and Design Processes for Remote Teams with Kevin Hale
Hey guys, welcome to the podcast! How’s it going? Great! Cool. Kevin, welcome back! For people who don’t know you, what do you do? I’m a partner at Y Combinator. I founded a company called Wufoo back in 2006. I was in the second batch at YC. That company…
Inflection points from graphs of function & derivatives | AP Calculus AB | Khan Academy
What we’re going to do in this video is try to get a graphical appreciation for inflection points, which we also cover in some detail in other videos. So the first thing to appreciate is an inflection point is a point on our graph where our slope goes fr…
Genetics vocabulary | Inheritance and variation | Middle school biology | Khan Academy
We know that any sexually reproducing organism is getting DNA from both its male parent and its female parent, and that’s true also for human beings. You might know we have 23 pairs of chromosomes, but let’s zoom in on one of those pairs. So, let’s say th…
"Where Love Is Illegal": Chronicling LGBT Stories of Love and Discrimination (Part 3) | Nat Geo Live
Our activism is continuing to evolve. In the next phase of Where Love Is Illegal, we are enduring to leverage our storytelling skills so we can further amplify the voices of LGBTQI+ communities around the world. And we’re doing just that in Jamaica. Last …
Dog Duty Inspiration | Big Fish, Texas
Yeah, it’s uh, Nick. Ores is Tommy or Arthur around? Pops brought Jenny and dropped her. Brought the fish house with me, ‘cause ultimately knows that I’m going to take care of her. I’m the only responsible one down there. She just sits there on a desk an…
Potential energy | Energy | Middle school physics | Khan Academy
Hello everyone! Let’s talk about potential energy. Potential energy is energy that is stored in an object, and this energy is related to the potential or the future possibility for an object to have a different type of energy, like kinetic energy from mo…