# Distance Formula

## How Far Apart

Your task is to come up with a formula to find the distance between any two horizontal points. Use the applet down below to help you develop the formula. Point B will change the distance, Point A will change the starting point. Hint: Pay attention to the x-values.

## Formula

What formula did you come up with?

## How Far Apart Vertical

Now your task is to come up with a formula to determine how far apart any two vertical points are. Point A changes your starting point and point B will change the length. Hint: Pay attention the the y-values.

What formula did you come up with?

## Distance Formula

Using the applet below create a right triangle whose hypotenuse is AB. Now, use the Pythagorean theorem (), and the two formulas you just developed. Determine a formula for the distance between any two points on the coordinate plane. Hint: Distance is the hypotenuse of a right triangle. Hint: Your x-values should be represented with and . Hint: Your y-values should be represented with and .

What did you and your partner decide on for the distance formula?

Click check and see how you did! We will be discussing this as a class so write down any questions we have so we can discuss them together.