1 / 54

Distance and Midpoint Formulas on a Number Line and Coordinate Plane

Learn how to find the distance and midpoint using formulas on a number line and coordinate plane, with examples and real-world applications.

pgarner
Download Presentation

Distance and Midpoint Formulas on a Number Line and Coordinate Plane

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Splash Screen

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

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

  5. 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

  6. 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

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

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

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

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

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

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

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

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

  15. 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

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

  17. distance • irrational number • midpoint • segment bisector Vocabulary

  18. Concept

  19. 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: Example 1

  20. 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

  21. Use the number line to find AX. A. 2 B. 8 C. –2 D. –8 Example 1

  22. Use the number line to find AX. A. 2 B. 8 C. –2 D. –8 Example 1

  23. Concept

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

  25. Find Distance on a Coordinate Plane Example 2

  26. Find Distance on a Coordinate Plane CheckGraph the ordered pairs and check by using the Pythagorean Theorem. Example 2

  27. . Find Distance on a Coordinate Plane Example 2

  28. A.4 B. C. D. Find the distance between A(–3, 4) and M(1, 2). Example 2

  29. A.4 B. C. D. Find the distance between A(–3, 4) and M(1, 2). Example 2

  30. Concept

  31. 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

  32. Find Midpoint on a Number Line Simplify. Answer: Example 3

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

  34. DRAG RACING The length of a drag racing strip is mile long. How many feet from the finish line isthe midpoint of the racing strip? A. 330 ft B. 660 ft C. 990 ft D. 1320 ft Example 3

  35. DRAG RACING The length of a drag racing strip is mile long. How many feet from the finish line isthe midpoint of the racing strip? A. 330 ft B. 660 ft C. 990 ft D. 1320 ft Example 3

  36. Concept

  37. Find Midpoint in Coordinate Plane Answer: Example 4

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

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

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

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

  42. Midpoint Formula Midpoint Formula Find the Coordinates of an Endpoint Answer: Example 5

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

  44. Find the coordinates ofRifN (8, –3) is the midpointofRSandShas coordinates (–1, 5). A. (3.5, 1) B. (–10, 13) C. (15, –1) D. (17, –11) Example 5

  45. Find the coordinates ofRifN (8, –3) is the midpointofRSandShas coordinates (–1, 5). A. (3.5, 1) B. (–10, 13) C. (15, –1) D. (17, –11) Example 5

  46. UnderstandYou 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. Use Algebra to Find Measures Example 6

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

  48. Original measure Use Algebra to Find Measures Example 6

  49. Original measure Use Algebra to Find Measures Example 6

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

More Related