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Math Help - Perpendicular Line/Equation

  1. #1
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    Perpendicular Line/Equation

    Hi,

    I would be grateful if someone could confirm whether the equation of the line perpendicular to the line 10x + 7y = 11 which passes through points (-1, 3) is 7x - 10y = -37?

    If not, where have I gone wrong?!
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  2. #2
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    Quote Originally Posted by looking0glass View Post
    Hi,

    I would be grateful if someone could confirm whether the equation of the line perpendicular to the line 10x + 7y = 11 which passes through points (-1, 3) is 7x - 10y = -37?

    If not, where have I gone wrong?!

    you are right !
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  3. #3
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    Hello, looking0glass!

    You are right!


    You can check your own work . . .

    You have: . 7x - 10y \:=\:-37


    Is it perpendicular to 10x + 7y \:=\:15?

    Solve for y . . .

    Their line is: . y \:=\:\text{-}\tfrac{10}{7}x+\tfrac{15}{7}
    . . Its slope is: m_1 \:=\:\text{-}\tfrac{10}{7}

    Your line is: . y \:=\:\tfrac{7}{10}x + \tfrac{37}{10}
    . . Its slope is: m_2\:=\:\tfrac{7}{10}

    Since m_1\!\cdot\!m_2 \:=\:-1, the line are perpendicular.


    Does your line pass through (-1, 3) ?
    Does (-1,3) satisfy your equation?

    . . 7(-1) - 10(3) \:=\:-37 . . . Yes!


    Therefore, your equation is correct.

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