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Lesson 1.3 Distance and Midpoints

Lesson 1.3 Distance and Midpoints. Geometry CP Mrs. Mongold. Chapter 1 Foldable Flap 2. Distance Formulas Number Line. -3. 4. P. Q. Chapter 1 Foldable Flap 2. Distance Formulas Cont… Coordinate Plane

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Lesson 1.3 Distance and Midpoints

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  1. Lesson 1.3 Distance and Midpoints Geometry CP Mrs. Mongold

  2. Chapter 1 Foldable Flap 2 • Distance Formulas • Number Line -3 4 P Q

  3. Chapter 1 Foldable Flap 2 • Distance Formulas Cont… • Coordinate Plane • The distance d between two points with coordinates and

  4. Distance Examples • Number Line • Use the number line to find QR

  5. Answer The coordinates of Q and R are –6 and –3. QR = | –6 – (–3) | Distance Formula = | –3 | or 3 Simplify.

  6. Another Number Line Example • Use the number line to find AX

  7. Answer • The coordinates of A and X are -5 and 3 AX = |-5 – 3| Distance Formula AX = |-8| AX = 8

  8. More Distance Examples • Coordinate Plane • Find the distance between E and F

  9. Answer • The coordinates are E(-4, 1) and F(3, -1) • Label them

  10. Another Example • Find the distance between A and M

  11. Answer • The coordinates are A(-3, 4) and M(1, 2) • Label (-3, 4) and (1, 2), and

  12. Chapter 1 Foldable Flap 3 • Midpoint Formulas • Number Line • The coordinate of the midpoint of a segment with endpoints that have coordinates a and b is

  13. Chapter 1 Foldable Flap 3 • Coordinate Plane • The coordinates of the midpoint of a segment with endpoints that have coordinates and

  14. Midpoint Examples • The coordinates on a number line Y and O are 7 and -15 respectively. Find the coordinate of the midpoint of segment YO.

  15. Answer Coordinate of the midpoint of YO is -4

  16. More Examples • Find the coordinates of M, the midpoint of segment GH for G(8, -6) and H (-14, 12)

  17. Answers

  18. More Examples • Find the coordinates of the midpoint of segment XY if X(-2, 3) and Y(-8, -9)

  19. Answers • (-5, -3)

  20. What about working backwards? • Find the coordinates of D if E(-6, 4) is the midpoint of segment DF and F(-5, -3)

  21. Answer • Let D be • Let E be for the midpoint • Let F be • So….. The coordinates for point D are (-7, 11)

  22. More Examples • What is the measure of segment PR if Q is the midpoint of segment PR?

  23. Answer • If Q is the midpoint then segments PQ and QR are both equal to 6 – 3x • So, 2(6 – 3x) = 14x + 2 12 – 6x = 14x + 2 10 = 20x x = ½ PR = 14(1/2) + 2 = 7 + 2 = 9

  24. Last Example • What is the measure of segment AC if B is the midpoint of segment AC?

  25. Answer • 2(2a – 1) = 3a + 1 4a – 2 = 3a + 1 a = 3 AC = 3(3) + 1 AC = 10

  26. Ticket Out The Door • Find the distance and midpoint of segment AB for A(5, 12) and B(-4, 8)

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