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

Example finding distance with Pythagorean theorem


2m read
·Nov 11, 2024

We are asked what is the distance between the following points, so pause this video and see if you can figure it out. Well, there are multiple ways to think about it. The way I think about it is really to try to draw a right triangle where these points, where the line that connects these points, is the hypotenuse.

Then we can just use the Pythagorean theorem. Let me show you what I am talking about. So let me draw a right triangle here. So that is the height of my right triangle, and this is the width of my right triangle. Then, the hypotenuse will connect these two points.

I could use my little ruler tool here to connect that point and that point right over there. I'll color it in orange, so there you have it. I have a right triangle where the line that connects those two points is the hypotenuse of that right triangle.

Now, why is that useful? From this, can you pause the video and figure out the length of that orange line, which is the distance between those two points? Well, what is the length of this red line? Well, you can see it on this grid here. This is equal to 2; it's exactly 2 spaces.

You can even think about it in terms of coordinates. The coordinate of this point up here is negative 5, comma 8 (−5, 8). The coordinate here is x equals 4, y equals 6 (4, 6). So the coordinate over here is going to have the same y-coordinate as this point, so it's going to be negative 5, comma 6 (−5, 6).

Notice you have a change only in the y-direction, and you're changing by 2. Now, what's the length of this line? Well, you could count it out: 1, 2, 3, 4, 5, 6, 7, 8, 9. So it's 9. Or you could even say, hey look, we're only changing our x-value. We're going from x equals -5 to x equals 4, so we're going to increase by 9.

Now, all of that just sets us up so that we can use the Pythagorean theorem. If we call this C, well, we know that a squared plus b squared is equal to c squared, or we could say that 2 squared plus 9 squared is going to be equal to our hypotenuse squared, which I'm just calling C squared.

So 2 squared, that is 4, plus 9 squared is 81, and that's going to be equal to C squared. Thus, we get C squared is equal to 85. C squared is equal to 85, or C is equal to the principal root of 85.

Now, can I simplify that a bit? Let's see, how many times does 5 go into 85? It goes, let's see, it goes 17 times. So neither of those are perfect squares. Yeah, that's 50 plus 35. So yeah, I think that's about as simple as I can write it.

If you wanted to express it as a decimal, you could approximate it by putting this into a calculator and however precise you want your approximation to be. But that, over here, that's the length of this line, our hypotenuse in our right triangle.

But more importantly, for the question they're asking, the distance between those points.

More Articles

View All
Why Chasing Happiness is Pointless (The Hedonic Treadmill)
Centuries ago, Siddhartha Gautama was born a prince, with a prophecy declaring that he would become either a great king or a spiritual leader. His father didn’t like the idea of his son walking the spiritual path; he wanted him to become a powerful ruler,…
Why I Don’t Feel Guilty for Busting Wildlife Traffickers | Nat Geo Live
(Onkuri speaks) Government agencies in many parts of the world either don’t know much about the problem of wildlife trafficking or they might be understaffed, they might be under-trained, they might be under-equipped. So, we go in to help them and supple…
Introduction by Kirsty Nathoo
Hi everyone, uh my name is Kirsty. Auu, I’m one of the partners at Y Combinator, and I would like to wish you a very warm welcome to this amazing venue for Startup School. This is our first International Startup School that we’ve done, so we’re very excit…
Civil society | Citizenship | High school civics | Khan Academy
Civil society is one of those terms that you might hear in a politician’s speech, maybe in a line about the importance of maintaining a strong relationship between the government and civil society. But what does it actually mean? A society that’s civilize…
Japanese Imperialism | World History | Khan Academy
What we’re going to discuss in this video is the evolution of Japan from being one of the most isolated countries in the world during the Tokugawa Shogunate to being the first Asian country to truly industrialize and become a world power. Historians will …
Pick Partners With Intelligence, Energy and Integrity
In terms of picking people to work with, I have high intelligence, high energy, and high integrity. I find that’s the three-part checklist that you cannot compromise on. You need someone who’s smart or they’re heading in the wrong direction, and you’re no…