# The Distance Between Two Points

When dealing with graphs, it’s important to understand how to find the distance between two points. This allows a student to determine how long the line is and can be advantageous in a variety of situations. The most common way to find the distance is to use the distance formula.

**Find the End Points and Determine Coordinates**

The end points for this type of problem will be given in written format or on a graph. The written format looks like (x1, y1) and (x2,y2). The numbers in this example are simply subscripts, meaning they’re just in place to differentiate between the two end points (end point 1 and end point 2).

If the If there is a graph, use that to determine the end points. It doesn’t matter which end point is used, as end point 1 and which is used as end point 2. They should simply be labeled like this to make it easier to tell which one is which in the next part of determining the distance.

**Use the Distance Formula to Find the Distance**

The next step in determining the distance between two points is to use the aptly named distance formula. This formula looks like this: d=√[(x2-x1)^+(y2-y1)^2]. This might look like a complex formula but, by following the order of operations, it can be easy to solve. Once the equation is solved, the student will know what the exact distance is between the two end points.

**Example Using the Distance Formula**

It can be helpful to see an example of this formula being used to see exactly how finding the distance is done. The example uses the end points of (2,3) and (5,7). To solve, use the first end point as (x1, y1), and the second end point as (x2, y2) for simplicity. Then, plug in these coordinates to the distance formula and solve for d.

d=√[(x2-x1)^2+(y2-y1)^2]

Fill in the coordinates in the equation:

d=√[(5-2)^2+(7-3)^2]

Solve the inner parenthesis first:

d=√[3^2+4^2]

Square both of the numbers by multiplying them with themselves:

d=√[9+16]

Add the numbers together:

d=√25

And finally, find the square root of the number.

d=5

For the end points of (2,3) and (5,7), the distance is going to be 5.

**Points to Remember**

The formula will always end with a positive number because of squaring the x coordinates and y coordinates before adding them together. A negative number squared means multiplying the negative by itself, which will result in a positive number. Additionally, the answer is not always going to be a whole number. It could be a decimal.

This might appear to be a complex formula that’s difficult to solve, but after practicing it a few times it becomes easy to do. Take the time to practice the above example without following along with the explanation to see if you get the right answer and to practice before moving on to more questions. You’ll see how easy it can be to simply follow the formula and find the right answer.