 This video will talk about the distance formula. This is our last video of the semester. Can you believe it? So we have the distance formula that says that d is equal to x2 minus x1 quantity squared plus y2 minus y1 quantity squared. And it's based on the idea that we have these two points x1, y1, and x2, y2. And remember the Pythagorean theorem, if we had a and b here, and we could say then that this length here would be the difference of my x's. And this is my y direction, so that's the difference of my y's. And let's just practice simplifying and then we'll work them in there. So the square root of 8 minus 5 would be 3 squared plus 5 minus 1 would be 4 and then squared. The square root of 9 plus 16, that ends up being the square root of 25. So the distance is 5 from that formula. Now let's use some extra points. This point right here, a is going to be 0, 0. And b is going to be the point 4, 3. It does not matter which is x1 and x2 and which is y1 and y2. So I typically use my first one as x1 and my second point is my 2's. So d is equal to the square root of the difference of my x's squared plus the difference of my y's squared. So my ax1 would be 0 or x2. It doesn't really matter which one and 4. And it doesn't even matter which one we start with. We just have to make sure that we're subtracting x's and subtracting y's because when you're square, the sign doesn't make any difference. And negative squared is still a positive. So this gives me negative 4 squared plus negative 3 squared. Negative 4 squared is 16 and negative 3 squared is 9. So again we're left with the square root of 25 and that's equal to 5. It just so happened that I had negatives this time but when I square them I still get 16 and 9. So what is the distance between these two points? Well let's try it. And we want the difference of the x's squared plus the difference of the y's squared. And there's a bunch of negatives in here so it really doesn't matter which order we go in. So negative 2 minus a negative 1 and negative 4 minus a negative 10. Didn't leave myself a whole lot of room there. So this will be square root of negative 2 plus a positive 1 is going to be negative 1 squared. And negative 4 minus a negative 10 will be plus 10 or 6 squared. This gives me 1 plus 36. I didn't really need my parentheses. Which will give me the square root of 37 and it's not a perfect square so we can just say the square root of 37. Right, one more. Final problem of the semester. Distance is equal to, and I've been taking the first one so just to be different I'm going to take the last term or last ordered pair and do it first. So 20 minus my 10 and 8 minus and then I have a negative 7 in here so I'll put it in parentheses. Equal to the square root of 20 minus 10 will be 10 that I have to square. And 8 plus 7 will be 15 which I'm going to have to square. And then this gives me the square root of 100 plus and I think I know what that is but I want to double check that I'm doing it right. So 15 carat 2 is 225. And if I add those I get 325 which I do not believe is a perfect square but again we could double check that. Second x squared 325 if it ends up a decimal then we know it wasn't a perfect square. So we are left with the square root of 325.