# Finding Midpoints of Line Segments Worksheets

A line segment is a part of line, and it has two endpoints that indicate the start and end of the segment. Because segments have a start and a finish, they have a definitive length. When a line segment finds itself placed on a Cartesian plane the position of the end points are defined by x and y coordinates. The midpoint of a segment is located hallway between the endpoints and on Cartesian plane the location of the midpoint would be described using x and y coordinates. There is a simple midpoint formula that we will learn in this section that takes into account both the x and y positions of the endpoints to help us declare a true midpoint. This selection of lessons and worksheets will help you learn how to evaluate line segments and find their true midpoint.

### Aligned Standard: High School Geometry - HSG-GPE.B.6

- Basic Step-by-step Lesson - We start out super easy to build some confidence for the more difficult problems.
- Guided Lesson - Number two will really throw you for a huge loop, if you let it!
- Guided Lesson Explanation - Number two is not that hard, if you just consider that it has a second dimension.
- Practice Worksheet - As my students use to say about this worksheet, "Easy-Hard-Easy-Hard!"
- Matching Worksheet - Don't get tripped up with this one.
- Midpoint of the Segment Worksheet Five Pack - It's all about that midpoint.
- Mid Point Segment Worksheet Five Pack - This one reminds me of the old battleship.

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

### Homework Sheets

Surprisingly, these are relatively simple for this level. Until you hit sheet number 3.

- Homework 1 - If the coordinate of A is x1 and the coordinate of B is x2, then the coordinate of the midpoint of AB is (x1 + x2) /2.
- Homework 2 - If you plot the midpoint on a strip of numbers, you can see that if the halfway between A and B.
- Homework 3 - B (5, 6) and C (-6, -5) are the endpoints of a segment. What is the midpoint M of that same segment?

### Practice Worksheets

These jump back and forth from being simple to being really complex.

- Practice 1 - What is the coordinate of the midpoint of EF?
- Practice 2 - B (7, -7) and C (-2, -5) are the endpoints of a segment. What is the midpoint M of that segment?
- Practice 3 - You don't have to use the formula in some cases here.

### Math Skill Quizzes

I have noted that on every test I have on the core curriculum this skill is always present.

- Quiz 1 - The of midpoint formula is M = ((x
^{1}+ x^{2})/2, ((y^{1}+ y^{2})/2) - Quiz 2 - Where M is the midpoint of a line segment with endpoint at (x
^{1},y^{1}) and (x^{2}, y^{2}. - Quiz 3 - Use the midpoint formula to find the midpoint M. Plug in A and B

### How to find the Midpoints of Line Segments

Let's hark back to basics: what is a line segment? A line segment is a line between two points. A line usually extends in both directions, but a segment has a definite length and fixed endpoints. Lines extend endlessly and hence have no point. But a line segment with defined endpoints has a midpoint. The endpoint are usually provided or given to us, but how do we find out the midpoints.

A midpoint of a line segment is the point that divides the line into exact halves. Finding the midpoint of the line segment is the same as finding the average of two numbers. For example, if you are asked to find the average of two numbers, 4 and 6, you will add both the numbers and divide them with two.

(4 + 6)/2 = 5 The midpoint formula works the same way. You have to find out the average of x-values and y-values of a line segment. To express it mathematically,

M = ((x1+x2)/(2 ), (y1+y2)/2) If you want to find out the midpoint of a segment with endpoint values (-4, -1) and y-values (2, 5). Put the values in the formula;

M = ((-4+2)/2, (-1+5)/2), M = ((-2)/2,4/2, M = (-1, 2)