When you want to find out how far apart two points are on a graph, there are some helpful steps you can use!

Imagine you have two points, ( A(x_1, y_1) ) and ( B(x_2, y_2) ), on a coordinate grid. To figure out the distance between them, we can use something called the Distance Formula. This formula is based on a math rule known as the Pythagorean theorem.

The Distance Formula

The formula to find the distance ( d ) between points ( A ) and ( B ) looks like this:

$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

Let’s see how this works step by step:

1. First, subtract the x-coordinates: ( (x_2 - x_1) ).
2. Next, subtract the y-coordinates: ( (y_2 - y_1) ).
3. Then, square both of those results (multiply each number by itself).
4. After that, add those squares together.
5. Finally, take the square root of that total.

Example

Now, let’s look at an example with points ( A(2, 3) ) and ( B(5, 7) ).

1. Start by calculating ( (5 - 2)^2 = 3^2 = 9 ).
2. Next, calculate ( (7 - 3)^2 = 4^2 = 16 ).
3. Now, add those squares together: ( 9 + 16 = 25 ).
4. Finally, find the square root of 25: ( \sqrt{25} = 5 ).

So, the distance between points ( A ) and ( B ) is 5 units!

This Distance Formula is really useful whenever you want to find how far apart any two points are on a coordinate grid.