## Finding Midpoints of Line Segments

#### Aligned To Common Core Standard:

**Expressing Properties** - HSG-GPE.B.6

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 line segment has a definite length and fixed endpoints. Lines extend endlessly hence have no point. But a line segment with defined endpoints has a midpoint. We know the endpoints of a line segment, but how do we find out the midpoints. Let's learn. Finding out the midpoint of a line segment: 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)

### Printable Worksheets And Lessons

- 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.

#### 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 the number line, 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 line segment. What is the midpoint M of that line 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 line segment. What is the midpoint M of that line segment?
- Practice 3 - You don't have to use the formula.

#### Math Skill Quizzes

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