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anonymous

  • one year ago

Find the circumcenter of triangle ABC with A(1,6), B(1,4), and C(5,4).

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  1. anonymous
    • one year ago
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    @jim_thompson5910

  2. jim_thompson5910
    • one year ago
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    |dw:1434588974015:dw|

  3. jim_thompson5910
    • one year ago
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    |dw:1434588988805:dw|

  4. jim_thompson5910
    • one year ago
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    Draw a segment from A to B |dw:1434589038187:dw|

  5. jim_thompson5910
    • one year ago
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    what is the midpoint of this segment?

  6. jim_thompson5910
    • one year ago
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    do you know the midpoint formula @iSpiffy2wice ?

  7. anonymous
    • one year ago
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    no I dont :/

  8. jim_thompson5910
    • one year ago
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    you add up the corresponding coordinates and then divide by 2

  9. jim_thompson5910
    • one year ago
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    midpoint of A and B x coordinate of A is 1 x coordinate of B is 1 add and divide by 2 (1+1)/2 = 2/2 = 1 so the x coord of the midpoint of AB is x = 1

  10. jim_thompson5910
    • one year ago
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    y coordinate of A is 6 y coordinate of B is 4 add and divide by 2 (6+4)/2 = 10/2 = 5 so the y coord of the midpoint of AB is y = 5

  11. jim_thompson5910
    • one year ago
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    midpoint of AB is (1,5) |dw:1434589451464:dw|

  12. jim_thompson5910
    • one year ago
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    making sense?

  13. anonymous
    • one year ago
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    yes it is

  14. jim_thompson5910
    • one year ago
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    so what is the midpoint of segment BC ?

  15. anonymous
    • one year ago
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    3,5/?

  16. jim_thompson5910
    • one year ago
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    B is (1,4) C is (5,4) x coords (x1+x2)/2 = (1+5)/2 = 6/2 = 3 y coords (y1+y2)/2 = (4+4)/2 = 8/2 = 4 the midpoint of BC is (3,4)

  17. jim_thompson5910
    • one year ago
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    |dw:1434589662988:dw|

  18. jim_thompson5910
    • one year ago
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    now that we have the midpoints of AB and BC, we construct the perpendicular bisectors of AB and BC |dw:1434589744838:dw|

  19. jim_thompson5910
    • one year ago
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    the perpendicular bisectors cross at (3,5) so that is the circumcenter |dw:1434589790411:dw|

  20. jim_thompson5910
    • one year ago
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    |dw:1434589818240:dw| my circle is a bit off since things aren't to scale but the circle is centered at (3,5), has a radius of 2 this circle goes through A,B and C

  21. anonymous
    • one year ago
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    thank you :O

  22. anonymous
    • one year ago
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    can you help me w/ another?

  23. jim_thompson5910
    • one year ago
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    sure, one more

  24. jim_thompson5910
    • one year ago
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    oh wait, the radius isn't 2, so ignore that portion

  25. anonymous
    • one year ago
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    is the attached file correct or no? D:

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  26. jim_thompson5910
    • one year ago
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    were you able to find the value of x? if so, what is x equal to?

  27. anonymous
    • one year ago
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    if were being honest no, I just guessed :/

  28. jim_thompson5910
    • one year ago
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    add up the three sides, and set that equal to 30 5x-7+3x+1+4x = 30 solve for x to get x = ??

  29. anonymous
    • one year ago
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    i have literally no idea what you just typed DD:

  30. jim_thompson5910
    • one year ago
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    the three sides are AB, BC, and AC |dw:1434590337740:dw|

  31. jim_thompson5910
    • one year ago
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    example: here is segment AB |dw:1434590361550:dw|

  32. jim_thompson5910
    • one year ago
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    I added up AB, BC, and AC then I set all that equal to 30 since that is the perimeter

  33. jim_thompson5910
    • one year ago
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    |dw:1434590403402:dw|

  34. jim_thompson5910
    • one year ago
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    are you able to solve 5x-7+3x+1+4x = 30 for x ?

  35. anonymous
    • one year ago
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    im trying but i dont really get it :/

  36. anonymous
    • one year ago
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    12x-6? :-/

  37. jim_thompson5910
    • one year ago
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    do you see how I did AB + BC + AC = perimeter ?

  38. jim_thompson5910
    • one year ago
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    yeah 12x - 6 = 30

  39. jim_thompson5910
    • one year ago
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    add 6 to both sides 12x - 6 = 30 12x - 6+6 = 30+6 12x+0 = 36 12x = 36

  40. jim_thompson5910
    • one year ago
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    what's next?

  41. anonymous
    • one year ago
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    BC??

  42. anonymous
    • one year ago
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    snt that what we do next :L

  43. jim_thompson5910
    • one year ago
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    well if 12 times ______ = 36, then what goes in the blank?

  44. anonymous
    • one year ago
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    3

  45. jim_thompson5910
    • one year ago
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    yep x = 3

  46. jim_thompson5910
    • one year ago
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    we then use this x value to find AB, BC, & AC

  47. jim_thompson5910
    • one year ago
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    For instance AB = 5x-7 AB = 5*3 - 7 ... replace x with 3 AB = 15 - 7 AB = 8 |dw:1434590785410:dw|

  48. jim_thompson5910
    • one year ago
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    what is the length of BC?

  49. anonymous
    • one year ago
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    it looks like an equilateral so 8 aswell? :L

  50. jim_thompson5910
    • one year ago
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    don't base things off the picture alone my picture isn't to scale

  51. jim_thompson5910
    • one year ago
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    use BC = 3x+1 and plug in x = 3

  52. anonymous
    • one year ago
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    34? ://

  53. jim_thompson5910
    • one year ago
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    BC = 3x+1 BC = 3*3+1 ... replace x with 3 BC = ???

  54. anonymous
    • one year ago
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    OH 10

  55. jim_thompson5910
    • one year ago
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    yep AB = 8 BC = 10 |dw:1434590954554:dw|

  56. jim_thompson5910
    • one year ago
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    and finally, how long is AC ?

  57. jim_thompson5910
    • one year ago
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    use the algebraic expression they give you

  58. anonymous
    • one year ago
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    12?

  59. jim_thompson5910
    • one year ago
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    good |dw:1434591008920:dw|

  60. jim_thompson5910
    • one year ago
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    Rule: with any triangle... the largest angle is opposite the largest side the smallest angle is opposite the smallest side

  61. anonymous
    • one year ago
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    so itd be |dw:1434590964987:dw| right?

  62. jim_thompson5910
    • one year ago
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    no

  63. jim_thompson5910
    • one year ago
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    |dw:1434591107541:dw|

  64. jim_thompson5910
    • one year ago
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    |dw:1434591138247:dw|

  65. anonymous
    • one year ago
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    C A B?

  66. jim_thompson5910
    • one year ago
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    correct

  67. jim_thompson5910
    • one year ago
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    In my drawing, all of the angles look the same (maybe 60 degrees?) but again, my drawing isn't to scale so it's not a good idea to base everything off the drawing alone

  68. jim_thompson5910
    • one year ago
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    if anything, the triangle probably looks like this |dw:1434591253370:dw|

  69. anonymous
    • one year ago
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    thanks for bearing with me and helping me!!

  70. jim_thompson5910
    • one year ago
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    you're welcome

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