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Math Help - perpendicular lines proof

  1. #1
    Senior Member furor celtica's Avatar
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    perpendicular lines proof

    two lines have equations y=m(1)x + c(1) and y = m(2)x + c(2), and m(1)m(2) = -1, proove that the lines are perpendicular.
    im aware that this is supposed to be an extension question but still i dont know what to use in order to proove this, seeing that m(1)m(2) = -1 is apparently not enough. can somebody help with a clear proof on how to do this?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by furor celtica View Post
    two lines have equations y=m(1)x + c(1) and y = m(2)x + c(2), and m(1)m(2) = -1, proove that the lines are perpendicular.
    im aware that this is supposed to be an extension question but still i dont know what to use in order to proove this, seeing that m(1)m(2) = -1 is apparently not enough. can somebody help with a clear proof on how to do this?
    Hmm. I am not sure if this would cut it. Let \vec{v}_1,\vec{v}_2 be vectors lying on the individual lines. We have that \vec{v}_1\cdot\vec{v}_2=0 since \vec{v}_1=(x,m_1x),\vec{v}_2=(y,m_2y) and thus we get \vec{v}_1\cdot\vec{v}_2=xy+m_1m_2xy=xy+-xy=0. Try to extend that. Does that seem feasible?
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  3. #3
    Senior Member furor celtica's Avatar
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    vectors are not involved in this section! i dont think that this method would pass, and (more importantly) i dont understand it. i'd need something pretty clear.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by furor celtica View Post
    vectors are not involved in this section! i dont think that this method would pass, and (more importantly) i dont understand it. i'd need something pretty clear.
    Ok. Well then this situation begs the question: what does perp. mean?
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  5. #5
    Senior Member furor celtica's Avatar
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    that the gradient of the lines, when multiplied, are equal to -1! thats how it is always conventionally defined, and that is why i am at a loss to prove it once this statement is no longer conclusive.
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  6. #6
    Senior Member furor celtica's Avatar
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    could the pythagorean theorem help in this case?
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  7. #7
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    Quote Originally Posted by furor celtica View Post
    two lines have equations y=m(1)x + c(1) and y = m(2)x + c(2), and m(1)m(2) = -1, proove that the lines are perpendicular.
    im aware that this is supposed to be an extension question but still i dont know what to use in order to proove this, seeing that m(1)m(2) = -1 is apparently not enough. can somebody help with a clear proof on how to do this?
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