1. Students will be able to find midpoint of a segment
Objective:
Students will be able to find midpoint of a segment
Students will be able to find the distance between 2 points.
Splash Screen

2. Mathematical Practices 2 Reason abstractly and quantitatively.
Content Standards
G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
Mathematical Practices
2 Reason abstractly and quantitatively.
7 Look for and make use of structure.
CCSS

3. You graphed points on the coordinate plane.
Find the distance between two points.
Find the midpoint of a segment.
Then/Now

4. distance
irrational number
midpoint
segment bisector
Vocabulary

5. Concept

6. Use the number line to find QR.
Find Distance on a Number Line
Use the number line to find QR.
The coordinates of Q and R are –6 and –3.
QR = | –6 – (–3) | Distance Formula
= | –3 | or 3 Simplify.
Answer: 3
Example 1

7. Use the number line to find AX.
C. –2
D. –8
Example 1

8. Concept

9. Find the distance between E(–4, 1) and F(3, –1).
Find Distance on a Coordinate Plane
Find the distance between E(–4, 1) and F(3, –1).
(x1, y1) = (–4, 1) and (x2, y2) = (3, –1)
Example 2

10. Find Distance on a Coordinate Plane
Check Graph the ordered pairs and check by using the Pythagorean Theorem.
Example 2

11. Find Distance on a Coordinate Plane.
Example 2

12. Find the distance between A(–3, 4) and M(1, 2).
Example 2

13. Concept

14. Find Midpoint on a Number Line
DECORATING Marco places a couch so that its end is perpendicular and 2.5 feet away from the wall. The couch is 90” wide. How far is the midpoint of the couch back from the wall in feet?
First we must convert 90 inches to 7.5 feet. The coordinates of the endpoints of the couch are 2.5 and 10. Let M be the midpoint of the couch.
Midpoint Formula
x1 = 2.5, x2 = 10
Example 3

15. Answer: The midpoint of the couch back is 6.25 feet from the wall.
Find Midpoint on a Number Line
Simplify.
Answer: The midpoint of the couch back is 6.25 feet from the wall.
Example 3

16. DRAG RACING The length of a drag racing strip is. mile long
DRAG RACING The length of a drag racing strip is mile long. How many feet from the finish line is the midpoint of the racing strip?
A. 330 ft
B. 660 ft
C. 990 ft
D ft
Example 3

17. Concept

18. Find Midpoint in Coordinate Plane
Answer: (–3, 3)
Example 4

19. A. (–10, –6)
B. (–5, –3)
C. (6, 12)
D. (–6, –12)
Example 4

20. Let D be (x1, y1) and F be (x2, y2) in the Midpoint Formula.
Find the Coordinates of an Endpoint
Let D be (x1, y1) and F be (x2, y2) in the Midpoint Formula.
(x2, y2) = (–5, –3)
Write two equations to find the coordinates of D.
Example 5

21. Answer: The coordinates of D are (–7, 11).
Find the Coordinates of an Endpoint
Midpoint Formula
Midpoint Formula
Answer: The coordinates of D are (–7, 11).
Example 5

22. Find the coordinates of R if N (8, –3) is the midpoint of RS and S has coordinates (–1, 5).
B. (–10, 13)
C. (15, –1)
D. (17, –11)
Example 5

23. Use Algebra to Find Measures
Understand You know that Q is the midpoint of PR, and the figure gives algebraic measures for QR and PR. You are asked to find the measure of PR.
Example 6

24. Plan Because Q is the midpoint, you know that
Use Algebra to Find Measures
Plan Because Q is the midpoint, you know
that
Use this equation and the algebraic measures to find a value for x.
Solve
Subtract 1 from each side.
Example 6

25. Use Algebra to Find Measures
Original measure
Example 6

26. QR = 6 – 3x Original Measure
Use Algebra to Find Measures
Check
QR = 6 – 3x Original Measure
Example 6

27. Use Algebra to Find Measures
Multiply.
Simplify.
Example 6

28. A. 1
B. 10
C. 5
D. 3
Example 6

29. Homework
Page 31 (14-30 even, even, 47-48, 53-54