Chapter 6
Graphing Functions
Section 6-1
Distance in the Coordinate Plane
Essential Questions

How do you use the distance formula to find the distance
between two points?

How do you use the midp...
Vocabulary
1. Coordinate Plane:


2. Quadrants:

3. x-axis:

4. y-axis:

5. Ordered Pairs:

6. Origin:
Vocabulary
1. Coordinate Plane: Two number lines drawn perpendicular to each
    other

2. Quadrants:

3. x-axis:

4. y-ax...
Vocabulary
1. Coordinate Plane: Two number lines drawn perpendicular to each
    other; used for graphing points

2. Quadr...
Vocabulary
1. Coordinate Plane: Two number lines drawn perpendicular to each
    other; used for graphing points

2. Quadr...
Vocabulary
1. Coordinate Plane: Two number lines drawn perpendicular to each
    other; used for graphing points

2. Quadr...
Vocabulary
1. Coordinate Plane: Two number lines drawn perpendicular to each
    other; used for graphing points

2. Quadr...
Vocabulary
1. Coordinate Plane: Two number lines drawn perpendicular to each
    other; used for graphing points

2. Quadr...
Vocabulary
1. Coordinate Plane: Two number lines drawn perpendicular to each
    other; used for graphing points

2. Quadr...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 1

 The vertices of rectangle ABCD are as follows: A = (-2, -2),
B = (4, -2), C = (4, 5), and D = (-2, 5). Find th...
Example 2

Find the distance between the points (0, 4) and (4, 0).
Example 2

Find the distance between the points (0, 4) and (4, 0).
Example 2

Find the distance between the points (0, 4) and (4, 0).
Example 2

Find the distance between the points (0, 4) and (4, 0).
Example 2

Find the distance between the points (0, 4) and (4, 0).
Example 2

Find the distance between the points (0, 4) and (4, 0).

                                         2   2    2
  ...
Example 2

Find the distance between the points (0, 4) and (4, 0).

                                         2   2    2
  ...
Example 2

Find the distance between the points (0, 4) and (4, 0).

                                         2   2    2
  ...
Example 2

Find the distance between the points (0, 4) and (4, 0).

                                         2   2    2
  ...
Example 2

Find the distance between the points (0, 4) and (4, 0).

                                         2   2        ...
Example 2

Find the distance between the points (0, 4) and (4, 0).

                                         2   2        ...
Example 2

Find the distance between the points (0, 4) and (4, 0).

                                         2   2        ...
Example 2

Find the distance between the points (0, 4) and (4, 0).

                                         2   2        ...
Distance Formula:




Midpoint Formula:
Distance Formula: d = (x1 − x2 )2 +( y1 − y2 )2 , for points (x1 , y1 ),(x2 , y2 )




Midpoint Formula:
Distance Formula: d = (x1 − x2 )2 +( y1 − y2 )2 , for points (x1 , y1 ),(x2 , y2 )

   This is nothing more than the Pytha...
Distance Formula: d = (x1 − x2 )2 +( y1 − y2 )2 , for points (x1 , y1 ),(x2 , y2 )

   This is nothing more than the Pytha...
Distance Formula: d = (x1 − x2 )2 +( y1 − y2 )2 , for points (x1 , y1 ),(x2 , y2 )

   This is nothing more than the Pytha...
Example 3
The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                 C = (-2, -1), and D = (5, 1).
 ...
Example 3
The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                 C = (-2, -1), and D = (5, 1).
 ...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Example 3
    The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2),
                     C = (-2, -1), and D = (...
Homework
Homework



                  p. 246 #1-33 odd, 18, 34, 36




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Distance in the Coordinate Plane

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  • Integrated Math 2 Section 6-1

    1. 1. Chapter 6 Graphing Functions
    2. 2. Section 6-1 Distance in the Coordinate Plane
    3. 3. Essential Questions How do you use the distance formula to find the distance between two points? How do you use the midpoint formula? Where you’ll see this: Geography, market research, community service, architecture
    4. 4. Vocabulary 1. Coordinate Plane: 2. Quadrants: 3. x-axis: 4. y-axis: 5. Ordered Pairs: 6. Origin:
    5. 5. Vocabulary 1. Coordinate Plane: Two number lines drawn perpendicular to each other 2. Quadrants: 3. x-axis: 4. y-axis: 5. Ordered Pairs: 6. Origin:
    6. 6. Vocabulary 1. Coordinate Plane: Two number lines drawn perpendicular to each other; used for graphing points 2. Quadrants: 3. x-axis: 4. y-axis: 5. Ordered Pairs: 6. Origin:
    7. 7. Vocabulary 1. Coordinate Plane: Two number lines drawn perpendicular to each other; used for graphing points 2. Quadrants: Four areas created by the coordinate plane 3. x-axis: 4. y-axis: 5. Ordered Pairs: 6. Origin:
    8. 8. Vocabulary 1. Coordinate Plane: Two number lines drawn perpendicular to each other; used for graphing points 2. Quadrants: Four areas created by the coordinate plane 3. x-axis: The horizontal axis on the coordinate plane 4. y-axis: 5. Ordered Pairs: 6. Origin:
    9. 9. Vocabulary 1. Coordinate Plane: Two number lines drawn perpendicular to each other; used for graphing points 2. Quadrants: Four areas created by the coordinate plane 3. x-axis: The horizontal axis on the coordinate plane 4. y-axis: The vertical axis on the coordinate plane 5. Ordered Pairs: 6. Origin:
    10. 10. Vocabulary 1. Coordinate Plane: Two number lines drawn perpendicular to each other; used for graphing points 2. Quadrants: Four areas created by the coordinate plane 3. x-axis: The horizontal axis on the coordinate plane 4. y-axis: The vertical axis on the coordinate plane 5. Ordered Pairs: Give us points in the form (x, y) 6. Origin:
    11. 11. Vocabulary 1. Coordinate Plane: Two number lines drawn perpendicular to each other; used for graphing points 2. Quadrants: Four areas created by the coordinate plane 3. x-axis: The horizontal axis on the coordinate plane 4. y-axis: The vertical axis on the coordinate plane 5. Ordered Pairs: Give us points in the form (x, y) 6. Origin: The point (0, 0), which is where the x-axis and y-axis meet
    12. 12. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD.
    13. 13. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. A
    14. 14. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. A B
    15. 15. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. C A B
    16. 16. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. D C A B
    17. 17. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. D C A B
    18. 18. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. D C AB = 4 −(−2) A B
    19. 19. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. D C AB = 4 −(−2) = 4 + 2 A B
    20. 20. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. D C AB = 4 −(−2) = 4 + 2 = 6 A B
    21. 21. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. C D AB = 4 −(−2) = 4 + 2 = 6 = 6 A B
    22. 22. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. C D AB = 4 −(−2) = 4 + 2 = 6 = 6 AD = 5−(−2) A B
    23. 23. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. C D AB = 4 −(−2) = 4 + 2 = 6 = 6 AD = 5−(−2) = 5+ 2 A B
    24. 24. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. C D AB = 4 −(−2) = 4 + 2 = 6 = 6 AD = 5−(−2) = 5+ 2 = 7 A B
    25. 25. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. C D AB = 4 −(−2) = 4 + 2 = 6 = 6 AD = 5−(−2) = 5+ 2 = 7 = 7 A B
    26. 26. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. C D AB = 4 −(−2) = 4 + 2 = 6 = 6 AD = 5−(−2) = 5+ 2 = 7 = 7 A B Area = lw
    27. 27. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. C D AB = 4 −(−2) = 4 + 2 = 6 = 6 AD = 5−(−2) = 5+ 2 = 7 = 7 A B Area = lw = 6(7)
    28. 28. Example 1 The vertices of rectangle ABCD are as follows: A = (-2, -2), B = (4, -2), C = (4, 5), and D = (-2, 5). Find the area of ABCD. C D AB = 4 −(−2) = 4 + 2 = 6 = 6 AD = 5−(−2) = 5+ 2 = 7 = 7 A B Area = lw = 6(7) = 42 square units
    29. 29. Example 2 Find the distance between the points (0, 4) and (4, 0).
    30. 30. Example 2 Find the distance between the points (0, 4) and (4, 0).
    31. 31. Example 2 Find the distance between the points (0, 4) and (4, 0).
    32. 32. Example 2 Find the distance between the points (0, 4) and (4, 0).
    33. 33. Example 2 Find the distance between the points (0, 4) and (4, 0).
    34. 34. Example 2 Find the distance between the points (0, 4) and (4, 0). 2 2 2 a +b =c
    35. 35. Example 2 Find the distance between the points (0, 4) and (4, 0). 2 2 2 a +b =c 2 2 2 0−4 + 4−0 = c
    36. 36. Example 2 Find the distance between the points (0, 4) and (4, 0). 2 2 2 a +b =c 2 2 2 0−4 + 4−0 = c 2 2 2 4 +4 = c
    37. 37. Example 2 Find the distance between the points (0, 4) and (4, 0). 2 2 2 a +b =c 2 2 2 0−4 + 4−0 = c 2 2 2 4 +4 = c 2 16+16 = c
    38. 38. Example 2 Find the distance between the points (0, 4) and (4, 0). 2 2 2 a +b =c 2 2 2 0−4 + 4−0 = c 2 2 2 4 +4 = c 2 16+16 = c 2 32 = c
    39. 39. Example 2 Find the distance between the points (0, 4) and (4, 0). 2 2 2 a +b =c 2 2 2 0−4 + 4−0 = c 2 2 2 4 +4 = c 2 16+16 = c 2 32 = c 2 c = ± 32
    40. 40. Example 2 Find the distance between the points (0, 4) and (4, 0). 2 2 2 a +b =c 2 2 2 0−4 + 4−0 = c 2 2 2 4 +4 = c 2 16+16 = c 2 32 = c 2 c = ± 32 c = 32
    41. 41. Example 2 Find the distance between the points (0, 4) and (4, 0). 2 2 2 a +b =c 2 2 2 0−4 + 4−0 = c 2 2 2 4 +4 = c 2 16+16 = c 2 32 = c 2 c = ± 32 c = 32 units
    42. 42. Distance Formula: Midpoint Formula:
    43. 43. Distance Formula: d = (x1 − x2 )2 +( y1 − y2 )2 , for points (x1 , y1 ),(x2 , y2 ) Midpoint Formula:
    44. 44. Distance Formula: d = (x1 − x2 )2 +( y1 − y2 )2 , for points (x1 , y1 ),(x2 , y2 ) This is nothing more than the Pythagorean Formula solved for c. Midpoint Formula:
    45. 45. Distance Formula: d = (x1 − x2 )2 +( y1 − y2 )2 , for points (x1 , y1 ),(x2 , y2 ) This is nothing more than the Pythagorean Formula solved for c.  x1 + x2 y1 + y2  Midpoint Formula: M =  ,  , for points (x1 , y1 ),(x2 , y2 )  2 2 
    46. 46. Distance Formula: d = (x1 − x2 )2 +( y1 − y2 )2 , for points (x1 , y1 ),(x2 , y2 ) This is nothing more than the Pythagorean Formula solved for c.  x1 + x2 y1 + y2  Midpoint Formula: M =  ,  , for points (x1 , y1 ),(x2 , y2 )  2 2  This is nothing more than averaging the x and y coordinates.
    47. 47. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). a. What kind of quadrilateral does ABCD appear to be?
    48. 48. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). a. What kind of quadrilateral does ABCD appear to be? A
    49. 49. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). a. What kind of quadrilateral does ABCD appear to be? A B
    50. 50. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). a. What kind of quadrilateral does ABCD appear to be? A B C
    51. 51. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). a. What kind of quadrilateral does ABCD appear to be? A B D C
    52. 52. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). a. What kind of quadrilateral does ABCD appear to be? A B D C
    53. 53. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). a. What kind of quadrilateral does ABCD appear to be? A This quadrilateral appears B to be a parallelogram D C
    54. 54. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. A B D C
    55. 55. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 AB = (2 −(−5)) +(4 − 2) A B D C
    56. 56. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 AB = (2 −(−5)) +(4 − 2) = (7) +(2) A B D C
    57. 57. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 AB = (2 −(−5)) +(4 − 2) = (7) +(2) A B = 49+ 4 D C
    58. 58. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 AB = (2 −(−5)) +(4 − 2) = (7) +(2) A B = 49+ 4 = 53 D C
    59. 59. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 AB = (2 −(−5)) +(4 − 2) = (7) +(2) A B = 49+ 4 = 53 units D C
    60. 60. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 AB = (2 −(−5)) +(4 − 2) = (7) +(2) A B = 49+ 4 = 53 units D CD = (−2 −5)2 +(−1−1)2 C
    61. 61. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 AB = (2 −(−5)) +(4 − 2) = (7) +(2) A B = 49+ 4 = 53 units D 2 2 2 2 CD = (−2 −5) +(−1−1) = (−7) +(−2) C
    62. 62. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 AB = (2 −(−5)) +(4 − 2) = (7) +(2) A B = 49+ 4 = 53 units D 2 2 2 2 CD = (−2 −5) +(−1−1) = (−7) +(−2) C = 49+ 4
    63. 63. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 AB = (2 −(−5)) +(4 − 2) = (7) +(2) A B = 49+ 4 = 53 units D 2 2 2 2 CD = (−2 −5) +(−1−1) = (−7) +(−2) C = 49+ 4 = 53
    64. 64. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 AB = (2 −(−5)) +(4 − 2) = (7) +(2) A B = 49+ 4 = 53 units D 2 2 2 2 CD = (−2 −5) +(−1−1) = (−7) +(−2) C = 49+ 4 = 53 units
    65. 65. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. A B D C
    66. 66. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 BC = (−5−(−2)) +(2 −(−1)) A B D C
    67. 67. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 BC = (−5−(−2)) +(2 −(−1)) = (−3) +(3) A B D C
    68. 68. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 BC = (−5−(−2)) +(2 −(−1)) = (−3) +(3) A B = 9+ 9 D C
    69. 69. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 BC = (−5−(−2)) +(2 −(−1)) = (−3) +(3) A B = 9+ 9 = 18 D C
    70. 70. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 BC = (−5−(−2)) +(2 −(−1)) = (−3) +(3) A B = 9+ 9 = 18 units D C
    71. 71. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 BC = (−5−(−2)) +(2 −(−1)) = (−3) +(3) A B = 9+ 9 = 18 units D 2 2 AD = (2 −5) +(4 −1) C
    72. 72. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 BC = (−5−(−2)) +(2 −(−1)) = (−3) +(3) A B = 9+ 9 = 18 units D 2 2 2 2 AD = (2 −5) +(4 −1) = (−3) +(3) C
    73. 73. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 BC = (−5−(−2)) +(2 −(−1)) = (−3) +(3) A B = 9+ 9 = 18 units D 2 2 2 2 AD = (2 −5) +(4 −1) = (−3) +(3) C = 9+ 9
    74. 74. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 BC = (−5−(−2)) +(2 −(−1)) = (−3) +(3) A B = 9+ 9 = 18 units D 2 2 2 2 AD = (2 −5) +(4 −1) = (−3) +(3) C = 9+ 9 = 18
    75. 75. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 BC = (−5−(−2)) +(2 −(−1)) = (−3) +(3) A B = 9+ 9 = 18 units D 2 2 2 2 AD = (2 −5) +(4 −1) = (−3) +(3) C = 9+ 9 = 18 units
    76. 76. Example 3 The vertices of quadrilateral ABCD are A = (2, 4), B = (-5, 2), C = (-2, -1), and D = (5, 1). b. Use distances to justify your guess. 2 2 2 2 BC = (−5−(−2)) +(2 −(−1)) = (−3) +(3) A B = 9+ 9 = 18 units D 2 2 2 2 AD = (2 −5) +(4 −1) = (−3) +(3) C = 9+ 9 = 18 units It is a parallelogram, as opposite sides are equal.
    77. 77. Homework
    78. 78. Homework p. 246 #1-33 odd, 18, 34, 36 “If I have seen further it is by standing on the shoulders of giants.” - Isaac Newton

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