1. Distance and Midpoints
Concept 13
Distance and Midpoints

2. Five-Minute Check (over Lesson 1–2) CCSS Then/Now New Vocabulary
Key Concept: Distance Formula (on Number Line)
Example 1: Find Distance on a Number Line
Key Concept: Distance Formula (in Coordinate Plane)
Example 2: Find Distance on Coordinate Plane
Key Concept: Midpoint Formula (on Number Line)
Example 3: Real-World Example: Find Midpoint on Number Line
Key Concept: Midpoint Formula (in Coordinate Plane)
Example 4: Find Midpoint in Coordinate Plane
Example 5: Find the Coordinates of an Endpoint
Example 6: Use Algebra to Find Measures
Lesson Menu

3. What is the value of x and AB if B is between A and C, AB = 3x + 2, BC = 7, and AC = 8x – 1?
A. x = 2, AB = 8
B. x = 1, AB = 5 C.
D. x = –2, AB = –4
5-Minute Check 1

4. If M is between L and N, LN = 3x – 1, LM = 4, and MN = x – 1, what is the value of x and MN?
A. x = 1, MN = 0
B. x = 2, MN = 1
C. x = 3, MN = 2
D. x = 4, MN = 3
5-Minute Check 2

5. Find RT. A. B. C. D. .
in.
5-Minute Check 3

6. What segment is congruent to MN?
A. MQ
B. QN
C. NQ
D. no congruent segments
5-Minute Check 4

7. What segment is congruent to NQ?
A. MN
B. NM
C. QM
D. no congruent segments
5-Minute Check 5

8. A. 5
B. 6
C. 14
D. 18
5-Minute Check 6

9. 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

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

11. Concept

12. 1. Use the number line to find QR.
Find Distance on a Number Line
1. 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

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

14. Concept

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

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

17. Midpoint – a point that is in the middle of 2 points, halfway between each point.
PQ = QR
PR = 2(PQ)
PR = 2(QR)

18. Concept

19. Answer: The midpoint of couch back is 6.25 feet from the wall.
Find Midpoint on a Number Line
5. 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
Simplify.
Answer: The midpoint of couch back is 6.25 feet from the wall.
Example 3

20. 6. The length of a drag racing strip is. mile long
6. 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

21. Concept

22. Find Midpoint in Coordinate Plane7.
Answer: (–3, 3)
Example 4

23. 8.
A. (–10, –6)
B. (–5, –3)
C. (6, 12)
D. (–6, –12)
Example 4

24. Let D be (x1, y1) and F be (x2, y2) in the Midpoint Formula.
Find the Coordinates of an Endpoint 9.
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

25. 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

26. 10. 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

27. Use Algebra to Find Measures
11.
Example 6

28. 12.
A. 1
B. 10
C. 5
D. 3
Example 6

29. Segment Bisector – a segment or line that goes through the middle of a segment, can create a midpoint.

30. End of the Lesson