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Homework Help: The slope of a bisector

  1. Aug 31, 2009 #1
    1. The problem statement, all variables and given/known data

    A, B, and C, are points (1,2), (0,0), and (-1,3) respectively.

    2. Relevant equations

    Find the slope of the bisector of angle ABC.

    3. The attempt at a solution

    I have done the following and dont know how it helpsL

    -found length of BA, BC, and AC
    -found the slope of BA, and BC
    -i dont know where to go from here

    The length of BA is √5

    The length of BC is √10

    The length of AC is √5

    The slope of BA is 2

    The slope of BC is -3

    Please do not do the work for me, i just need some advice as to what to do from here.
  2. jcsd
  3. Aug 31, 2009 #2
    P.S. this is probably not precalculus, but this is problem that was in my precalculus book (i think we a re reviewing from algebra).

    i forgot so much from last year:confused:
  4. Aug 31, 2009 #3
    I'm not quite sure how'd one would go about doing this problem without a bit of trigonometry, but for starters, the segment AC has slope -1/2 and is therefore perpendicular to AB. Hence CAB is a right triangle (i.e. angle CAB is a right angle). This forces the distance of AC to be sqrt(15) (This is verifiable even if CAB isn't right).

    But since CAB is a right triangle then the tangent of angle ABC is [itex]\sqrt(15)/\sqrt(5) =\sqrt(3)[/itex]. This along with a well timed tangent angle sum indentity should get you the answer.

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