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
Lecture 1 - How to Start a Startup (Sam Altman, Dustin Moskovitz)
Welcome. Um, can they turn this on? Maybe all right. Uh, people here in the back, can you guys hear me? Is the mic on? No? Uh, maybe you can ask them to turn it on. Maybe we can get a bigger—ah, there we go. All right. Maybe we can get a bigger auditorium…
Why do midterm congressional elections matter? | US government and civics | Khan Academy
[Narrator] Why do midterm congressional elections matter? Congressional elections matter because they are often, and have increasingly been, a referendum on the president. So, it is a kind of real test from real voters doing real voting about whether pe…
Whole number divided by a fraction example
Let’s see if we can figure out what four divided by two-thirds is. And like always, pause this video and see if you can figure it out on your own. Well, one way to approach it is to realize that this is the same thing as four times the reciprocal of two-…
China's Economy is Failing.
Recently, one of the world’s largest superpowers, that of course being China, reported a rather worrying economic statistic that shows just how much the Chinese economy is struggling after their extensive lockdowns. Last Wednesday, the world’s second larg…
Introduction to the cell | Cells | High school biology | Khan Academy
You might already have some type of a notion of what a cell is. You might already realize that it is the most basic unit of life. Some would argue that maybe viruses are even a more basic unit of life. But the organisms that we consider living, like ourse…
WALL STREET LOSSES! - The TRUTH Behind GameStop, WallStreetBets & Robinhood | Kevin O'Leary
Everybody had just completely discounted. Thought it didn’t matter, and the Robin Hood investors, “Ah, we don’t care about them; they’re too young, they have no money.” Well, that’s not how it is. I can’t stand the arrogance of sophisticated Wall Street i…