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
Protecting the Queendoms 👑 | Queens | National Geographic
The most impressive female leaders will stop at nothing. Orca matriarchs will go to great lengths to make sure their sons thrive. The matriarch’s family has met up with another pod. She needs her son to mate and pass on her genes. One female in the visit…
Warren Buffett Just Invested $4.1 BILLION in a New Stock!
Well, here we go again, everyone. We’ve waited patiently, and now we finally get an updated peek into the portfolios of the world’s best investors. The 13F filings are live, everybody! And for those that don’t know what a 13F is, I feel like we’ve been he…
Strategy in solving quadratic equations | Quadratic functions & equations | Algebra I | Khan Academy
[Instructor] In this video, we’re gonna talk about a few of the pitfalls that someone might encounter while they’re trying to solve a quadratic equation like this. Why is it a quadratic equation? Well, it’s a quadratic because it has this second degree …
The Current State of the Stock Market (2021)
So that right there is Charlie Monkey. He’s essentially Warren Buffett’s right hand man. He is the vice chairman of Berkshire Hathaway. What we’re looking at right here is him giving a talk at the Daily Journal shareholders meeting, which happened a coupl…
r greater than g but less inequality
One of the core ideas of Thomas Piketty’s book is if the return on capital is greater than the growth in economy, then that could drive inequality. Inequality is a natural byproduct of a market capitalist economy, and one could argue that, hey, look, some…
Standard normal table for proportion between values | AP Statistics | Khan Academy
A set of laptop prices are normally distributed with a mean of 750 and a standard deviation of 60. What proportion of laptop prices are between 624 and 768 dollars? So let’s think about what they are asking. We have a normal distribution for the prices, …