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5-Minute Check 1

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 = 3 x + 2, BC = 7, and AC = 8 x – 1?. 5-Minute Check 1. Concept. Find Midpoint on a Number Line.

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5-Minute Check 1

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  1. 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

  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. Find Midpoint on a Number Line Simplify. Answer: The midpoint of the couch back is 6.25 feet from the wall. Example 1

  5. 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? Think, Write, Pair, Share A. 330 ft B. 660 ft C. 990 ft D. 1320 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. (x2, y2) = (–5, –3) Find Missing Coordinates Let D be (x1, y1) and F be (x2, y2) in the Midpoint Formula. Write two equations to find the coordinates of D. Example 3

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

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

  13. 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. Use Algebra to Find Measures Example 4

  14. Because 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. Example 4

  15. Original measure Use Algebra to Find Measures Example 4

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

  17. Multiply. Simplify. Use Algebra to Find Measures 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 = |-2 - -6| 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)

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