# Finding the Length of Line Segments Worksheets

Geometry is one of those crazy areas of study that bore you when you are studying them, but they have a profound affect on your real situations. To most students this is one of those topics that just presents like a puzzle and do not hold a great level of meaning to their existence. The truth is that there are so many different scenarios where this skill could be critical for you. Suppose you were working on an old home and trying to determine how to best reinforce the structure and integrity of your home. You will find many structural supports that are buried within walls and the foundation. If you were able to understand the location of their endpoints, you could easily determine their length and then make decisions based on it to reinforce your home. That may be an extreme example, but a profound one. This series of worksheets will use the coordinate plane to help students decipher the length of line segments.

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

- Distance Formula Step-by-Step Lesson- We give you two point in the coordinate plane and ask you to the length of the line they create.
- Guided Lesson - What's the length of the line between points A and B?
- Guided Lesson Explanation - A healthy helping of distance formula to get your day started.
- Practice Worksheet - They have a little bit of change between the way each question is worded, but in the end they are the same question.
- Matching Worksheet - Match the distance of the lines to the points that can create a line of that length.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Use the end points to determine the length.

- Homework 1 - We can use the distance formula to determine the length of this line.
- Homework 2 - The distance formula asks us to take the square root of (x
_{2}- x_{1})^{2}+ (y_{2}- y_{1})^{2} - Homework 3 - Find the length of the line segment whose endpoints are: (-5, 5) and (14, 10).

### Practice Worksheets

The distance formula is something we encourage students to memorize. It is not often given on standard tests.

- Practice 1 - Find the distance between the points (9, -9) and (8, 7)
- Practice 2 - Where is the point in your mind?
- Practice 3 - You can also use geometry to find this one.

### Math Skill Quizzes

All the questions are positioned in the way you will see them on assessments. There are really only two formats that we have seen.

- Quiz 1 - Don't forget what the negative value tells us.
- Quiz 2 - Please yourself forward with these.
- Quiz 3 - Where should I move with these values?

### What Is the Distance Formula?

The distance formula is a useful tool to find the distance between two arbitrarily points. The formula is divided from the Pythagoras theorem which is the a^{2}+b^{2}= c^{2}, where c is the longest side of a right-angled triangle. This can be adapted to be used within a coordinate plane. We can use this to find measures of just about anything that is straight and forms a triangular structure. This has endless application in industry and manufacturing.

Suppose you are given two points (-2, 1) and (1, 5), which are located on different locations of the axes. In the present example, the x coordinate is on the negative x-axis, and the ordinate is on the positive y-axis. While both of the coordinates like on the positive side of the x and y-axis. You would work this through the distance formula that is presented as:

d = √((x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2})

To process this equation, you begin by finding the difference between the coordinates.

(x_{2} - x_{1}) = (1 - -2) = 3

(y_{2} - y_{1}) = (5 - 1) = 4

When we pop this into the equation, now that we know the differences. It would result use in squaring the results and summing them up as:

(3)^{2} + (4)^{2} = 9 + 16 = 25

If we take the square of that value, we have determined the distance: √ 25 = 5