# Distance Formula Worksheets

This is a neat trick that you can use to find the distance between two points that are found on a coordinate system. If you identify two ordered pairs, they are separated by two distances the x-axis and the y-axis. We could represent these differences in distance by drawing lines for each axis. These lines will meet at a point of origin and form an angle. You can draw a line that connects those lines forming the hypotenuse of a triangle. If we determine the length of that hypotenuse, we have determined the distance between those points. Students learn how to use and manipulate the distance formula through the help of these worksheets and lessons.

### Aligned Standard: HSG.GPE.B.7

- Using Ordered Pairs Step-by-Step Lesson- Mr. and Mrs. Patterson are trying to get home and they are halfway there.
- Guided Lesson - We look at using the formula to define the size of line segments as well as the distance between two points.
- Distance Formula Guided Lesson Explanation - The explanation presents two concepts to students on distance and halfway
- Ordered Pair Worksheet 1 - Find the distance between two of the points.
- All Skills Review Worksheet 2 - Find the distance between two points, use graphs, and answer a word problem.

- Identify and Determine Distance 4-Pack - This is a pack of four worksheets plus answers to work on the specific purpose of the unit.
- Answer Keys - These are for all the unlocked materials above.

### Practice Sheets

We run the full gamut of problem types here.

- Practice 1 - Find the distance between the two points. Leave answers in radical form.
- Practice 2 - This a graphing form that you will need to measure and interpret by yourself.
- Practice 3 - In this one, you are just given two ordered pairs to work off of.

### Homework Sheets

The answers are rolled in there for you. We suggest giving the answers to students for a single version and then make them work for the other two.

- Homework 1 - More ordered pair work.
- Homework 2 - Put that formula to work.
- Homework 3 - Show all of your own work.

### Math Skill Quizzes

Each quiz is successively more difficult.

- Quiz 1 - These lines are similar, just spaced out differently.
- Quiz 2 - Some of these points are way out there.
- Quiz 3 - Mark each statement as TRUE or FALSE. Match the two points with the appropriate distance.

### What is the Distance Formula?

Distance formula is a useful tool that helps in finding the distance the between two existing points on a Cartesian plane. These points can be arbitrarily represented as (x_{1}, x_{2}) and (y_{1}, y_{2}).

The distance formula in itself is actually a formula that has been derived from the famous Pythagoras theorem commonly used in geometry. The Pythagoras theorem is a^{2} + b^{2} = c^{2}. C in this case, is the longest side of a right-angled triangle which is also called a hypotenuse. A and B are shorted sides and are also called legs of the right angle. The essence of the distance formula is for calculating the hypotenuse of the right angle which is mostly represented by the letter c in Pythagoras theorem.

The distance formula is : D = √ [(x_{1} - x_{2}) + (y_{1} - y_{2})]

### How You Can Use This Skill in Your Life?

When students understand how this concept can be applied to their everyday life, it will hold a lot more value and motivate them to master the concept. When it comes to the distance formula, it is a skill that helps us gauge an unknown distance that we are trying to understand. Just the other day I was buying a ladder for my home. I needed to figure out how big of a ladder I needed. I pondered all the different reasons that I needed to have a ladder and figure out the situation where I would need the biggest ladder. I have a holiday decorations area in the foyer of my home. It eighteen feet to the ledge of the foyer. An eighteen-foot ladder would not do the trick because a completely vertical ladder would not hold. I determined that the ladder would need to be a minimum of eight feet from the ledge to hold my weight also allowing for those extra holiday pounds. Using this formula, I determined that I would need a twenty-five-foot ladder. This calculation can be applied to any situation where you are trying to determine a missing length. It lends itself to all forms of transportation and travel. I also use it to get an idea of how much gas I will need to make long trips, but I do cheat and use Google Maps that automatically does the calculations for me.