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Perpendicular lines

  1. Mar 22, 2008 #1
    Determine a constant real number k such that the lines AB and CD are perpendicular.
    A(1,2), B(4,0), C(k,2), D(1,-3). (answer given is k=-3/2)

    If two lines are perpendicular the product of their slopes is -1.

    The slope of AB is [tex]\frac{0-2}{4-1}[/tex] = [tex]\frac{-2}{3}[/tex]

    The slope of CD is [tex]\frac{-3-2}{1-k}[/tex] = [tex]\frac{-5}{1-k}[/tex]
    I set the product of these slopes equal to -1 and solve for k.

    [tex]\frac{-2}{3}[/tex] x [tex]\frac{-5}{1-k}[/tex]=-1
    10=3(k-1)
    10=3k-3
    13=3k
    13/3=k
    This is not the answer given and I am not seeing my error. Any help would be appreciated.
    Latex question. The = sign and x symbol don't line up well with the rest of the equations in the first half of my post. How can I correct that?
     
  2. jcsd
  3. Mar 22, 2008 #2
    Your k value is correct ...

    [tex]\frac{0-2}{4-1}=\frac{-2}{3}[/tex]

    Check my LaTeX ...
     
    Last edited: Mar 22, 2008
  4. Mar 22, 2008 #3
    Thanks for the help.
     
  5. Mar 24, 2008 #4
    Verified using an alternate method (direction cosines and perpendicularity) to confirm that your answer is correct.
     
  6. Mar 24, 2008 #5
    You are 100% correct, reporting the text book error might be helpful for the rest using the same book...
     
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