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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. What segment is congruent to MN ?. A. MQ B. QN C. NQ D. no congruent segments.

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

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

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

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

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

  7. Concept

  8. 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

  9. Can distance ever be negative?

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

  11. You will need a scientific calculator to do this problem • Put x’s and y’s in the formula • Subtract x’s and square • Subtract y’s and square • Add numbers under the radical • Take square root if answer is in decimal form. Concept

  12. (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

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

  14. . Find Distance on a Coordinate Plane Example 2

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

  16. Add the x’s and divide by 2 • Add the y’s and divide by 2 Concept

  17. Assignment Day 1 p. 31, 13-31 odd No work, No credit!

  18. 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

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

  20. 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 1 mile = 5280 feet Example 3

  21. Concept

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

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

  24. (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

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

  26. 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

  27. 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

  28. 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

  29. Original measure Use Algebra to Find Measures Example 6

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

  31. Multiply. Simplify. Use Algebra to Find Measures Example 6

  32. A. 1 B. 10 C. 5 D. 3 Example 6

  33. Segment Bisector A segment bisector is any segment, line, or line that intersects a segment at its midpoint .

  34. Construction: Bisect a Segment • Draw a segment. • Place the compass on one end and open the compass bigger than half of the segment. • Draw arcs above and below the segment. • Without moving the compass sixe, move the point to the other end of the segment. • Draw arcs about and below the segment. • Use a straightedge to connect the x’s you made above and below the segment. • Where this new segment crosses the 1st one is the midpoint. • See page 30 for pictures.

  35. Assignment 1-3 p. 31, 28-30 even, 33-55 odd No work, No credit

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