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Math Help - Help with line slope proof

  1. #1
    danb
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    Help with line slope proof

    Hi, I am stuck on a geometry problem and it's really frustrating, it concerns the proof to the theorem that says "If two nonvertical lines are perpendicular, the product of their slopes is -1."

    Now, this might be considered an algebra problem, but in the exercise I have to find the answer to:

    Please let me know if I need to include more information or anything if this seems vague, it's probably an easy problem but I just don't understand how to get the correct answer, thanks.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by danb View Post
    Hi, I am stuck on a geometry problem and it's really frustrating, it concerns the proof to the theorem that says "If two nonvertical lines are perpendicular, the product of their slopes is -1."
    this is a wierd question, two lines are perpendicular when the product of their slopes are -1, period. doesn't matter if they are nonvertical or not. what tools do you have to use in this proof?


    Now, this might be considered an algebra problem, but in the exercise I have to find the answer to:

    Please let me know if I need to include more information or anything if this seems vague, it's probably an easy problem but I just don't understand how to get the correct answer, thanks.
    ok, so we just do manipulations on the first equation so one side ends up looking like BD/DC, the other side should have some manipultions on m. here goes:

    -DC/BD = m ...............BD/DC is positive, so make that side positive
    => DC/BD = -m ..........i just multiplied through by -1
    => BD/DC = -1/m ........i took the inverse, so now one side looks like what we wanted and the other side tells us what it is in terms of m
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Jhevon View Post
    this is a wierd question, two lines are perpendicular when the product of their slopes are -1, period. doesn't matter if they are nonvertical or not.
    I'm afraid it does. The "slope" of a vertical line is a/0 where a is some real number. The slope of a horizontal line is 0, but (a/0)*0 is undefined, not -1.

    -Dan
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    Quote Originally Posted by topsquark View Post
    I'm afraid it does. The "slope" of a vertical line is a/0 where a is some real number. The slope of a horizontal line is 0, but (a/0)*0 is undefined, not -1.
    It seems to me you are getting more careful in mathematics. Is that true?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    It seems to me you are getting more careful in mathematics. Is that true?
    I know I'm getting more careful
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by topsquark View Post
    I'm afraid it does. The "slope" of a vertical line is a/0 where a is some real number. The slope of a horizontal line is 0, but (a/0)*0 is undefined, not -1.

    -Dan
    so how would you prove that a vertical and a horiztontal line are perpendicular? represent the lines by vectors and using the dot product maybe? or use a line to connect two arbitrary points and show that the pythagorean theorem holds for the resulting triangle?
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    Quote Originally Posted by Jhevon View Post
    so how would you prove that a vertical and a horiztontal line are perpendicular?
    Theorem:Any two non-vertical lines are perpendicular if and only if the product of the slopes is -1.

    Proof:Trivial.

    Now, that theorem is true. Vertical lines do not apply to it.

    Your question seems to be how can a vertical and horizontal line be parallel if they are not included in the theorem? But that no matter it one is talking about non-vertical lines.

    You can show it like this.

    Theorem:Let y=k be any vertical line, let x=j be any horizontal line. Then the two lines are perpendicular.

    Proof:Line y=k is paralle with the x-axis (basically given). Line x=j is perpendicular with x-axis (they way you define rectangular coordinates are in terms of perpendicular and parallels so this and the statement before are basically given to us). Since x=j is perpendicular to a line parallel with y=k thus,
    x=j is perpendicular with y=k.
    Q.E.D.
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