1. 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

2. Concept

3. 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 1

4. 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 1

5. Think, Write, Pair, Share
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 1

6. Concept

7. Concept

8. Find Midpoint in Coordinate Plane
Answer: (–3, 3)
Example 2

9. Think, Write, Pair, Share
A. (–10, –6)
B. (–5, –3)
C. (6, 12)
D. (–6, –12)
Example 2

10. Let D be (x1, y1) and F be (x2, y2) in the Midpoint Formula.
Find Missing Coordinates
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 3

11. Answer: The coordinates of D are (–7, 11).
Find Missing Coordinates
Midpoint Formula
Midpoint Formula
Answer: The coordinates of D are (–7, 11).
Example 3

12. Think, Write, Pair, Share
Find the coordinates of R if N (8, –3) is the midpoint of RS and S has coordinates (–1, 5).
A. (3.5, 1)
B. (–10, 13)
C. (15, –1)
D. (17, –11)
Example 3

13. Use Algebra to Find Measures
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 4

14. Because Q is the midpoint, you know that
Use Algebra to Find Measures
Because Q is the midpoint, you know that
Use this equation and the algebraic measures to find a value for x.
Subtract 1 from each side.
Example 4

15. Use Algebra to Find Measures
Original measure
Example 4

16. QR = 6 – 3x Original Measure
Use Algebra to Find Measures
QR = 6 – 3x Original Measure
Example 4

17. Use Algebra to Find Measures
Multiply.
Simplify.
Example 4

18. Think, Write, Pair, Share
A. 1
B. 10
C. 5
D. 3
Example 4

19. Locating a Point at Fractional Distances
BD = |x2 – x1| Distance Formula
= | | x1 = -6, x2 = -2
= |4| or 4 Subtract.
The distance between B and D is 4.
Example 5

20. Locating a Point at Fractional Distances
Answer: -5
Example 5

21. Think, Write, Pair, Share
A. -7
B. 0
C. 2
D. -1
Example 5

22. Fractional Distances on a Coordinate Plane
Example 6

23. Example 6

24. Answer: P (–1.3, -1)
Example 6

25. Think, Write, Pair, Share
A. (2, 1.8)
B. (-2, -1.8)
C. (-1.8, -2)
D. (1.8, 2)
Example 6

26. Locating a Point Given a Ratio

27. Locating a Point Given a Ratio
Answer: F (–2, 4.4)

28. Think, Write, Pair, Share
A. (3, -0.4)
B. (3, 0.4)
C. (-0.4, 8.9)
D. (-0.4, 3.1)