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Outline. Collect syllabi Go over daily quiz Answer homework questions (markings?) Daily Quiz Lecture 1.3. Front Side – True or False. Back Side. Use the diagram to answer the questions. 9. Name one pair of opposite rays. ____________ & ____________. Opposite Rays

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Outline

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  1. Outline • Collect syllabi • Go over daily quiz • Answer homework questions (markings?) • Daily Quiz • Lecture 1.3

  2. Front Side – True or False

  3. Back Side Use the diagram to answer the questions. 9. Name one pair of opposite rays. ____________ & ____________ • Opposite Rays • Share the same end point • The 2 rays are on the same line • They go in opposite directions

  4. Back Side Use the diagram to answer the questions. 10. Name three lines that intersect at C. _____________ _____________ _____________

  5. Homework Questions • Did you circle the ones you got wrong? • Did you come to class prepared to ask questions? • If so, which ones did you get wrong? • Are you ready for the Daily Quiz?

  6. Daily Quiz 1.2 – Back side Notice that there is no back…. a. Give two other names for b. Name 3 points that are collinear. c. What is the intersection of line a and line XY? d. What is the intersection of plane C and Plane D? e. Give another name for YX f. Name a pair of opposite rays

  7. WARM-UP Directions: Find x. What do you notice about the relationship between segment AB and segment BC?

  8. 1.3 Lesson Use Midpoint and Distance Formulas

  9. Midpoint The midpoint of a segment is a point that divides a segment into 2 congruent segments. I I A B M So….. AM = MB

  10. Segment Bisector A point, segment, line, or plane that divides a line segment into two equal parts I I I I I I

  11. Skateboard In the skateboard design, VWbisects XYat point T, and XT=39.9cm. Find XY. Point Tis the midpoint of XY . So, XT = TY = 39.9 cm. Bisect: to cut in 1/2 EXAMPLE 1 Find segment lengths SOLUTION XY = XT + TY Segment Addition Postulate = 39.9 + 39.9 Substitute. = 79.8cm Add.

  12. ALGEBRA Point Mis the midpoint of VW. Find the length of VM . STEP 1 Write and solve an equation. Use the fact that that VM = MW. EXAMPLE 2 Use algebra with segment lengths SOLUTION VM= MW Write equation. 4x–1= 3x + 3 Substitute. x – 1 = 3 Subtract 3xfrom each side. x = 4 Add 1 to each side.

  13. STEP 2 Evaluate the expression for VMwhen x = 4. So, the length of VMis 15. Check: Because VM = MW, the length of MWshould be 15. If you evaluate the expression for MW, you should find that MW = 15. MW = 3x + 3 = 3(4) +3 = 15 EXAMPLE 2 Use algebra with segment lengths VM = 4x – 1 = 4(4) – 1 = 15

  14. GUIDED PRACTICE linel Identify the segment bisector of . Then find PQ.

  15. MIDPOINT FORMULA The midpoint of two points P(x1, y1) and Q(x2, y2) is M(X,Y) = M(x1 + x2, x2 +y2) 2 2 Think of it as taking the average of the x’s and the average of the y’s to make a new point.

  16. a. FIND MIDPOINTThe endpoints ofRSare R(1,–3) and S(4, 2). Find the coordinates of the midpoint M. EXAMPLE 3 Use the Midpoint Formula

  17. 1 , – , M M = 2 5 2 The coordinates of the midpoint Mare 1 5 – , 2 2 ANSWER – 3 + 2 1 + 4 2 2 EXAMPLE 3 Use the Midpoint Formula SOLUTION a. FIND MIDPOINTUse the Midpoint Formula.

  18. FIND ENDPOINTLet (x, y) be the coordinates of endpoint K. Use the Midpoint Formula. b. FIND ENDPOINTThe midpoint of JKis M(2, 1). One endpoint is J(1, 4). Find the coordinates of endpoint K. STEP 1 Find x. STEP 2 Find y. 4+ y 1+ x 1 2 = = 2 2 ANSWER The coordinates of endpoint Kare (3, – 2). EXAMPLE 3 Use the Midpoint Formula 4 + y = 2 1 + x = 4 y =–2 x =3

  19. Guided Practice A. The endpoints of are A(1, 2) and B(7, 8). Find the coordinates of the midpoint M. B. The midpoint of is M(– 1, – 2). One endpoint is W(4, 4). Find the coordinates of endpoint V.

  20. Distance Formula The distance between two points A and B is

  21. EXAMPLE 4 Standardized Test Practice SOLUTION Use the Distance Formula. You may find it helpful to draw a diagram.

  22. RS = 2 2 = (x– x) + (y–y) 2 1 2 1 = 2 2 [(4 – 2)] + [(–1) –3] = 2 2 (2) + (–4 ) = = 4+16 4.47 20 ANSWER The correct answer is C. EXAMPLE 4 Standardized Test Practice Distance Formula Substitute. Subtract. Evaluate powers. Add. Use a calculator to approximate the square root.

  23. Example 5 Amy lives 4 blocks north and 6 blocks east of the school. Seth lives 2 blocks south and 7 blocks west of the same school. How far away does Amy live from Seth?

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