So, before we get started, I need to define some things.

**Right Triangle**:

A right triangle is a triangle with a right angle.

**Pythagorean Theorem
**The Pythagorean Theorem says that . and are the two shorter sides of the right triangle. The long side is called the hypotenuse. From now on we will refer to as . If we want to get , instead of , we can do

Ok. Now that we’re done with that, we can start actually calculating distance. This part is pretty simple. Imagine we have a cat that wants to get to a mouse, but needs to know how far away it is. The cat is at 0,0, and the mouse is at 5,5. Let’s call the cat’s x and y “cx” and “cy” , and let’s call the mouse’s x and y “mx” and “my”.In many of these equations, I will be using a lot. If a number is between those bars, it means that it will be made positive (). First, we find , and we find . These are the differences between the x values and the y values. Now we take those numbers (let’s call them “dx” and “dy”). To get , we do . Now we can do . We are done. is our distance. This seems long, but we just produced a short formula to find distance. Here is the completed formula:

For those of you still having trouble, this might help explain why you can’t just add dx and dy, and why you are using right triangles: