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Math Help - How to find the equation of a line perpendicular to another?

  1. #1
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    How to find the equation of a line perpendicular to another?

    How does y+2=0 rearrange to y=-2? And how do you find a perpendicular line (with a given coordinate)?
    a = 0,1
    b = 10,6
    Equation = y=1/2x+1

    Find the equation of the line perpendicular to AB passing through B.

    Please explain all in a 'step-to-step' fashion in the simplest way possible including any rearranging equations etc.
    I know the answer (y=-2x+26) but, other than the negative reciprocal, I'm not sure how to get it. My answer on the exam was 'y=-2x+6' so I went wrong at the end.
    Thanks a lot!
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: How to find the equation of a line perpendicular to another?

    How does y+2=0 rearrange to y=-2?
    If you are given:

    y+2=0

    and you want to solve for y, then since 2 is being added to y, we may isolate y by subtracting 2 from both sides:

    y+2-2=0-2

    y=-2

    And how do you find a perpendicular line (with a given coordinate)?
    You are given the points:

    A(0,1),B(10,6)

    The perpendicular slope is found by:

    -\frac{\Delta x}{\Delta y}=-\frac{10-0}{6-1}=-\frac{10}{5}=-2

    We now have the slope of the line and the point it passes through, so using the point-slope formula, we find the equation of the line is:

    y-6=-2(x-10)

    y=-2x+26
    Last edited by MarkFL; September 22nd 2012 at 09:43 AM.
    Thanks from Ashir
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  3. #3
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    Re: How to find the equation of a line perpendicular to another?

    Ah, understood, thanks.

    I can't catch on the last bit. Is there an easier way or could you explain how you got to that?
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: How to find the equation of a line perpendicular to another?

    y-6=-2(x-10)

    y-6=(-2)(x)-(-2)(10)

    y-6=-2x+20

    y-6+6=-2x+20+6

    y=-2x+26
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  5. #5
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    Re: How to find the equation of a line perpendicular to another?

    I'm really sorry but I still can't understand it. Where did -6 come from? Where did -10 come from? Why was the '-2' moved?
    Could you explain the format of the above expressions please? And what is this 'point-slope formula'? y=mx+c or?
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: How to find the equation of a line perpendicular to another?

    The point-slope formula states that given the point (x_1,y_1) on a line and the slope m, then the equation of the line is:

    y-y_1=m(x-x_1)

    The -2, which is the slope, was distributed to both terms within the parentheses.
    Thanks from Ashir
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  7. #7
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    Re: How to find the equation of a line perpendicular to another?

    I understand now, but is there another way to do it? I don't think I'll remember that. I have trouble remembering that a line sloping to the left is +ve and to the right -ve (not even sure that's correct)
    Or is there any way to relate that formula to y=mx+c? Or is there another formula altogether? I know how to get the slope, so is there another way to get the y intercept (c)?
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  8. #8
    MHF Contributor MarkFL's Avatar
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    Re: How to find the equation of a line perpendicular to another?

    Yes, use the formula for slope with the points (10,6) and (0,c):

    -2=\frac{c-6}{0-10}

    c-6=20

    c=26
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  9. #9
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    Re: How to find the equation of a line perpendicular to another?

    My friend taught me an easier way. Substitute 'y' and 'x' with the coords of the point it passes through (B)

    6=-2(10)+C
    6=-20+C
    26=C

    Thanks for the help though!
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