1. Math II 7.2 Line Segments

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

3. Midpoint for number lines6 10
The midpoint for AB is found by adding a and b then dividing by 2
6 + 10 2

4. Midpoint for number lines-2 4
The midpoint for AB is found by adding a and b then dividing by 2
-2 + 4 2

5. What if it’s not a flat line?
That’s
why we just
Learned about
The coordinate plane B

6. What if it’s not a flat line?
(x,y) A
We just
need the
X and y coordinates
For each end
(x,y) B

7. That is kind of confusing
(x1,y1)
(x,y) A
We have
Two points
So let’s change
How we label them
(x2,y2)
(x,y) B

8. Here is your formula
( , )
X1 + X2 2
Y1 + Y2 2

9. If this is easier for you
( , )
Add X’s 2
Add Y’s 2

10. (1,8)
( , )
2 2 A
(4, 6)
( , )
X1 + X2 Y1 + Y2
(7,4) B
( , )

11. (-3,6)
( , )
2 2 A
(1, -2)
( , )
X1 + X2 Y1 + Y2
(5,-10) B
( , )

12. MIDPOINT Y1 + Y2 X1 + X2 2 2 (x1,y1) First, We are finding
The middle of the
X’s
Then
We are finding
The middle of the
Y’s
And that
gives us the
MIDPOINT
(x2,y2) B

13. Constructing a Midpoint

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

15. Word of the day
Congruent

16. What does “Congruent” mean?
if two thing have the same value, we say they are equal.
If two things have the same shape we say they are congruent.

17. Congruent Symbol
= this guy means equal
= this guy means
congruent

18. Congruent Segments
Segments are congruent if, and only if, they have the same length.
So how do we know how long they are?

19. THE Distance Formula
D = (X2-X1)2 + (Y2-Y1)2
Duhn

20. D = (X2-X1)2 + (Y2-Y1)2 Distance Formula
X1 = x coordinate of 1st point
Y1 = y coordinate of 1st point
X2 = x coordinate of 2nd point
Y2 = y coordinate of 2nd point

21. How far is it from (1,2) to (3,4)
D = (X2-X1)2 + (Y2-Y1)2
D = (3-1)2 + (4-2)2
D = (2)2 + (2)2
D = 4 + 4
D = 8
D = 2.8

22. How far is it from (2,5) to (2,8)
D = (X2-X1)2 + (Y2-Y1)2
D = (2-2)2 + (8-5)2
D = (0)2 + (3)2
D = 0 + 9
D = 9
D = 3

23. How far is it from (-8,2) to (0,-4)
D = (X2-X1)2 + (Y2-Y1)2
D = (0--8)2 + (-4-2)2
D = (8)2 + (-6)2
D =
D = 100
D = 10

24. A good Midpoint Question2x
5x-6 P M Q
M is the midpoint of pq find the value of x?

25. A good Midpoint Question2x
5x-6 P M Q
Since m is the midpoint the PM = MQ
So 2x = 5x-6

26. A good Midpoint Question2x
5x-6 P M Q
2x = 5x-6 subtract 5x from both sides
-3x = -6 divide both sides by -3
X = 2

27. A good Midpoint Question2x
5x-6 P M Q
What if they ask for pm?
Since X = 2 plug that into 2x
2(2) = 4
What about pq?