Using the Distance Formula

In this article we are going to find the distance between two points using the distance formula. So this formula that we have written down is the distance formula, and here's how you read it. The distance is equal to the square root of x2 minus x1 squared plus y2 minus y1 squared. Where do these x2 and x1 and the y2 and y1 come from? They refer to the coordinates of the points. So before we even start off, we’re going to go ahead and label our points as point number one and point number two. This will help us keep them straight in the formula.

The next part is we’re going to write down this formula and leave those x's and y's blank for now so that we can fill them in later. So it says: take x2 minus x1. So we'll take the second x coordinate and subtract the first x coordinate. So 2 minus a minus 4. Let's do the same thing with the y. So y2 minus y1, second y coordinate minus the first y coordinate. Now, once you have everything plugged into the formula, it really just comes down to a matter of simplifying things.

We recommend starting from the inside and working your way out just to make sure you don't make an error. So 2 minus a minus 4 becomes a positive 6. Negative 3 minus 1 gives us a negative 4. Of course, both these numbers get squared. So 6 squared gives us a 36. Negative 4 squared gives us a 16. We can add those together and get the square root of 52.

Now, since the distance formula involves roots, you want to make sure that when you get to this point that if the root can be simplified that you go ahead and you do so. In fact 52, if we look at it and start to break it down, it's actually equal to 4 times 13. This means we can simplify this root into 2 times the square root of 13. Normally we'd be done because this number represents the exact distance between two points, but oftentimes when you're dealing with distance, it might be in a word problem and you're looking for the distance in miles or meters, and sometimes looking at this number doesn't really give us much of a hint in terms of how big it really is.

So we will actually take this, and we'll also get its decimal approximation. So you take 2 and the square root of 13 and you'll get that it is about equal to 7.211. There we go!