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Homework Help: Do you know how to find the equation of lines?

  1. May 4, 2010 #1
    1. The problem statement, all variables and given/known data
    http://img1.uploadscreenshot.com/images/orig/5/12317385174-orig.jpg"

    3. The attempt at a solution

    Points: (0, 0); ( [x/2], [x√3]/2 ); (x, 0)

    For points (0, 0) and ( [x/2], [x√3]/2 )

    Gradient = m = {[x√3]/2 - 0}/ {[x/2] - 0} = √3


    m = (y-0)/(x-0)
    √3 = y/x
    y = x√3 <--- eqn. 1


    For points ( [x/2], [x√3]/2 ) and (x, 0)

    Gradient = m = {0 - (x√3)/2}/ {x-(x/2)} = -√3


    m = [y - {(x√3)/2)] / [ x- (x/2) ]
    -√3 = [y - {(x√3)/2)] / [ x- (x/2) ]
    y = [(-x√3)/2] + [(x√3)/2]
    y = 0 <--- eqn. 2


    For points (0, 0) and (x, 0)

    Gradient = m = (0 - 0)/ (x-0) = 0


    m = (y - 0) / (x-0)
    0 = 0​

    If you went through all of the above you'll notice that I got two y=0 equations...Where did I mess up?
     
    Last edited by a moderator: Apr 25, 2017
  2. jcsd
  3. May 4, 2010 #2

    Mark44

    Staff: Mentor

    In the second pair of points. You found the slope to be -sqrt(3), but substituted +sqrt(3) when you found the equation.
     
    Last edited by a moderator: Apr 25, 2017
  4. May 4, 2010 #3
    Plugged in the wrong slope in the second equation. It should be negative.
     
  5. May 4, 2010 #4
    Mark, you genius!
     
  6. May 4, 2010 #5
    Sorry guys! That was a typo! I basically just copied the whole response off my copy. I did take -√3 as gradient for the second pair of equations.
     
  7. May 4, 2010 #6
    Oh, now I see. The problem is the redefinition of "x". As used in the coordinates, it is a constant. When used in "y=mx+b", it is a variable.

    Let's use the points (0,0) (a,0) and... whatever that third one was, but with "a" instead of "x". You'll get the right answer.
     
  8. May 4, 2010 #7
    Okay, now the first gradient becomes (-a√3) / (2x-a)... thanks Chaz! I hope this works.
     
    Last edited: May 4, 2010
  9. May 4, 2010 #8

    Mark44

    Staff: Mentor

    Well, we both spotted it at the same time.
     
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