**Video Transcript**

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Transcript
**The Distance Formula**

Deep in the Amazonian jungle, Carlos lives with his family in a teeny-tiny village. Carlos likes most things about his village, but he has to wake up at the crack of dawn if he wants to be at school on time. It’s not so much that his school is so far away, but there’s a huge canyon between the village and the school, so Carlos must walk around the canyon to get to his school. To make his journey faster, Carlos has a great idea. But to make sure his idea will work he’ll need to use the **Distance Formula**.

Take a look at this map The scale's in yards. Here’s the path that Carlos usually walks to go to school, around this side of the canyon, across the bridge, and then along the other side of the canyon. It takes Carlos about 2 hours to walk to school every day. So, what's Carlos' great idea? He wants to build a zip line to go right across the canyon, allowing him to get to school in a fraction of the time! But he doesn't have any rope. What can he do? In a stroke of genius, Carlos decides to use the rope from his mom's clothesline. There are just two problems with this plan: the clothesline is only **350 yards** long. Will that be enough? And what will his mom say about him using the rope from the clothesline to build the zip line?

### Using the Pythagorean Theorem to Calculate the Distance

To answer the first question, he needs to calculate the distance between these two points. As for Carlos' mom and the missing clothesline? Only time will tell...

We can't help Carlos out with his mom, but we can help him **solve** his little **math problem**. To find the **distance** between any two known points in a **coordinate plane**, first construct a **right triangle**. Then, modify the **Pythagorean Theorem** to solve for the **unknown distance**. Notice how we replaced 'a' and 'b' with the **quantities** 'x'-two minus 'x'-one and 'y'-two minus 'y'-one, respectively. Since 'c' is the **distance** we want to know, we'll now call this **variable** 'd'.

After taking the **square roots** of both sides of the **equation**, we're left with the **Distance Formula**. The location of Carlos' village is at the **ordered pair** one hundred, one hundred and the location of his school is at the ordered pair two hundred, four hundred. Carlos' home will be point 1 and his school will be point 2. Now, using the known points, we can replace the **variables** in the **expression** and solve for the **distance** Now that there are no more variables, we can finish this off with **PEMDAS** to get the distance. To get across the canyon, the zip line only needs to be approximately 316.23 yards...so Carlos has enough rope!

He's really excited to use the zip line for the first time, AND he was even able to sleep two hours longer than usual.

There he goes. Whe! Oh man, now Carlos knows a bit more about the villagers than he wanted.

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