1. Secondary Math 2
7.2 Line Segments

2. Warm-UP: Create a line, ray, or segment for each problem. (notes from 7.1)𝑃𝑄 𝑇𝑉 𝐴𝑀 𝐾𝑅

3. Questions on 7.1:

4. Find the AVERAGE of the following:
3 and 5
10 and 20
15 and 30
32 and 36

5. Midpoint for number linesA B
The midpoint for 𝐴𝐵 is found by adding A and B, then dividing by 2.
𝐴+𝐵 2

6. Midpoint for number lines3 5
The midpoint for 𝐴𝐵 is found by adding A and B, then dividing by 2.
3+5 2

7. Midpoint for number lines10 20
The midpoint for 𝐴𝐵 is found by adding A and B, then dividing by 2.

8. How about for non-horizontal lines?
Remember the coordinate plane? B

9. How about for non-horizontal lines?
(x, y) A
Remember the coordinate plane?
(x, y) B

10. How about for non-horizontal lines?
(x1, y1) A
Remember the coordinate plane?
(x2, y2) B

11. Finding the AVERAGE (the midpoint):
( 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 )
Add the x’s, and divide by 2.
Add the y’s, and divide by 2.

12. Let’s practice!!!
Find the midpoint (and graph it!)
( 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 )
( , )
(4,6)
Here’s what we’re doing

13. More Practice!!!

14. Midpoints Midpoints are in the exact middle of a line segment.
They cut the line segment into 2 equal pieces
Those pieces are congruent!!!!

15. What is congruent?
If two things have the same value, they are equal (=)
If two things have the same shape, we say they are congruent (≅)
Specific marks on the lines to show they are congruent

16. Congruent Segments
Line segments are congruent if, and only if, they have the same length.
How do we know how long they are?!?!?

17. THE Distance Formula
𝑫 = (𝒙𝟐−𝒙𝟏)𝟐 + (𝒚𝟐−𝒚𝟏)𝟐

18. 𝑫 = (𝒙𝟐−𝒙𝟏)𝟐 + (𝒚𝟐−𝒚𝟏)𝟐 THE Distance Formula
𝑫 = (𝒙𝟐−𝒙𝟏)𝟐 + (𝒚𝟐−𝒚𝟏)𝟐
x1= x coordinate of 1st point
y1= y coordinate of 1st point
x2= x coordinate of 2nd point
y2= y coordinate of 2nd point

19. Use the Distance Formula
How far is it from (1, 2) to (3, 4)
𝑫 = (𝒙𝟐−𝒙𝟏)𝟐 + (𝒚𝟐−𝒚𝟏)𝟐

20. Let’s Practice Some!

21. More Practice!

22. Midpoint Question M is the midpoint of 𝑃𝑄 . Find the value of x.
What is the length of 𝑃𝑀 ? What is the length of 𝑃𝑄 ?