Distance between 2 place

We're just moving straight right. This is the same distance as that distance right there. So to figure out that distance, it's literally the end x point. And you could actually go either way, because you're going to square everything, so it doesn't matter if you get negative numbers, so the distance here is going to be 6 minus 3, right? That's this distance right here, which is equal to 3. So we figured out the base. And to just remind ourselves, that is equal to the change in x.

That was equal to your finishing x minus your starting x. This is our delta x. Now, by the same exact line of reasoning, this height right here is going to be your change in y. Up here, you're at y is equal to 0.

That's kind of where you finish. That's your higher y point. And over here, you're at y is equal to negative 4. So change in y is equal to 0 minus negative 4. I'm just taking the larger y-value minus the smaller y-value, the larger x-value minus the smaller x-value. But you're going to see we're going to square it in a second, so even if you did it the other way around, you'd get a negative number, but you'd still get the same answer, so this is equal to 4. So this side is equal to 4.

You can even count it on the graph paper if you like. And this side is equal to 3. And now we can do the Pythagorean theorem. This distance is the distance squared. Be careful. The distance squared is going to be equal to this delta x squared, the change in x squared plus the change in y squared. This is nothing fancy. Sometimes people will call this the distance formula.

It's just the Pythagorean theorem. This side squared plus that side squared is equal to hypotenuse squared, because this is a right triangle. So let's apply it with these numbers, the numbers that we have at hand. So the distance squared is going to be equal to delta x squared is 3 squared plus delta y squared plus 4 squared, which is equal to 9 plus 16, which is equal to So the distance is equal to-- let me write that-- d squared is equal to So this distance right here is 5.

Or if we look at this distance right here, that was the original problem. How far is this point from that point? It is 5 units away. So what you'll see here, they call it the distance formula, but it's just the Pythagorean theorem. And just so you're exposed to all of the ways that you'll see the distance formula, sometimes people will say, oh, if I have two points, if I have one point, let's call it x1 and y1, so that's just a particular point.

And let's say I have another point that is x2 comma y2. Sometimes, you'll see this formula, that the distance-- you'll see it in different ways. But you'll see that the distance is equal to-- and it looks as though there's this really complicated formula, but I want you to see that this is really just the Pythagorean theorem. You see that the distance is equal to x2 minus x1 minus x1 squared plus y2 minus y1 squared. You'll see this written in a lot of textbooks as the distance formula.

And it's a complete waste of your time to memorize it because it's really just the Pythagorean theorem. This is your change in x. And it really doesn't matter which x you pick to be first or second, because even if you get the negative of this value, when you square it, the negative disappears. This right here is your change in y. So it's just saying that the distance squared-- remember, if you square both sides of this equation, the radical will disappear and this will be the distance squared is equal to this expression squared, delta x squared, change in x-- delta means change in-- delta x squared plus delta y squared.

I don't want to confuse you. Delta y just means change in y. I should have probably said that earlier in the video. But let's apply it to a couple more, and I'll just pick some points at random. Let's say I have the point, let's see, 1, 2, 3, 4, 5, 6. Negative 6 comma negative 4. And let's say I want to find the distance between that and 1 comma 1, 2, 3, 4, 5, 6, 7, and the point 1 comma 7, so I want to find this distance right here.

So it's the exact same idea. We just use the Pythagorean theorem. You figure out this distance, which is our change in x, this distance, which is our change in y. This distance squared plus this distance squared is going to equal that distance squared. So let's do it. Distance Between Cities Calculator This website allows you to find the distance between cities or any two places and get directions using Google maps.

The calculated distance will be shown in miles and kilometers. Using this tool is simple; you can enter two cities or location names and press the enter button to measure distance. It will show you distance calculation in different units, show routes on map, and provide different directions to reach the destination. What is Google Maps? Google Maps is basically free mapping service that enables us to explore the world map online with many interactive features.

What is Mileage Calculator? Mileage is basically a distance travelled in miles. Our tool can help you in estimating the mileage between two cities or locations. What is Distance Calculator? Distance calculator is used to measure the distance between two locations. With our web-based tool you can find the distance between two points on the map. How to find Driving Distance between two Cities? Finding KM or miles distance between two cities is easy with this tool you can simply origin city in "From" input field and destination city in "To" input field and press the Enter button.

On the next page you will see the estimated driving distance in miles, kilometers and nautical miles along with estimated travel time and best route for this trip.

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Distance calculator is used to measure the distance between two locations. With our web-based tool you can find the distance between two points on the map. How to find Driving Distance between two Cities? Finding KM or miles distance between two cities is easy with this tool you can simply origin city in "From" input field and destination city in "To" input field and press the Enter button.

On the next page you will see the estimated driving distance in miles, kilometers and nautical miles along with estimated travel time and best route for this trip. If you are planning to take a flight it also show the straight line or air distance in miles, kilometers and nautical miles. If you want to find the shortest distance between two locations you just have to enter both places in textboxes and press enter or click.

On next page you will see different suggested routes options with driving directions and route information. You can select the best and shortest route by comparing the travel time of suggested routes and directions shown at Google Maps. How to find Driving Directions between two Places? When you input two places names on our website it will show the driving direction in the suggested routes section. It will display the turning points and details of all the suggested routes, i.

How to plan your Trip using Distance Calculator? Using this distance calculator you can not only plan your trip in United States but all over the world. This tool measure and calculate distances, provides you information about your current and destination locations e. To find the return distance between two places, start by entering start and end locations in calculator control and use the Round Trip option or use the Calculate Return Distance option.

You can also try a different route while coming back by adding multiple destinations. How to find the fastest road distance between two places? This distance calculator can find the fastest distance between any two locations. Enter the source and destination to calculate the distance and then check for the fastest road distance between the two locations. Check map and driving directions of your route which helps you find the destination easier.

How to calculate the return distance between two places? To calculate the return distance between two places, start by entering start and end locations and then click on return distance to check the distance traveled in return. You can also check the return distance by other travel modes like bus, subway, tram, train and rail.