1. Locating Points and Midpoints
LESSON 1–3
Locating Points and Midpoints

2. Five-Minute Check (over Lesson 1–2) TEKS Then/Now New Vocabulary
Key Concept: Midpoint Formula (on Number Line)
Example 1: Real-World Example: Find Midpoint on Number Line
Key Concept: Midpoint Formula (in Coordinate Plane)
Example 2: Find Midpoint in Coordinate Plane
Example 3: Finding Missing Coordinates
Example 4: Find Missing Measures
Example 5: Locating a Point at Fractional Distances
Example 6: Fractional Distances on a Coordinate Plane
Example 7: Locating a Point Given a Ratio
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 Processes G.1(A), G.1(G)
Targeted TEKS
G.2(A) Determine the coordinates of a point that is a given fractional distance less than one from one end of a line
segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint.
G.2(B) Derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines.
Also addresses G.5(B).
Mathematical Processes
G.1(A), G.1(G)
TEKS

10. You found the distance between two points on a line segment.
Find the midpoint of a segment.
Locate a point on a segment given a fractional distance from one endpoint.
Then/Now

11. midpoint
segment bisector
Vocabulary

12. Concept

13. 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

14. 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

15. 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 1

16. Concept

17. Concept

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

19. A. (–10, –6)
B. (–5, –3)
C. (6, 12)
D. (–6, –12)
Example 2

20. 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

21. 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

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 3

23. 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

24. 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

25. Use Algebra to Find Measures
Original measure
Example 4

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

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

28. A. 1
B. 10
C. 5
D. 3
Example 4

29. 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

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

31. A. -7
B. 0
C. 2
D. -1
Example 5

32. Fractional Distances on a Coordinate Plane
Example 6

33. Example 6

34. Answer: P (–1.3, -1)
Example 6

35. A. (2, 1.8)
B. (-2, -1.8)
C. (-1.8, -2)
D. (1.8, 2)
Example 6

36. Locating a Point Given a Ratio

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

38. A. (3, -0.4)
B. (3, 0.4)
C. (-0.4, 8.9)
D. (-0.4, 3.1)

39. Locating Points and Midpoints
LESSON 1–3
Locating Points and Midpoints