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Math Help - perpendicular lines

  1. #1
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    perpendicular lines

    the question with the answers:
    perpendicular lines-untitled0.jpg
    perpendicular lines-untitled.jpg
    perpendicular lines-untitledb.jpg

    what i don't understand is this part:
    perpendicular lines-untitled1.jpg
    how did that happen?
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  2. #2
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    Re: perpendicular lines

    click to enlarge :O
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  3. #3
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    Re: perpendicular lines

    Quote Originally Posted by muddywaters View Post
    the question with the answers:
    Click image for larger version. 

Name:	untitled0.JPG 
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Size:	36.4 KB 
ID:	24153
    Click image for larger version. 

Name:	untitled.JPG 
Views:	8 
Size:	19.2 KB 
ID:	24154
    Click image for larger version. 

Name:	untitledb.JPG 
Views:	8 
Size:	34.6 KB 
ID:	24155

    what i don't understand is this part:
    Click image for larger version. 

Name:	untitled1.JPG 
Views:	11 
Size:	9.9 KB 
ID:	24156
    how did that happen?
    1. You know from equation 2:

    \displaystyle{y-y_0=-\frac1m(x-x_0)~\implies~(y-y_0)^2=\frac1{m^2}(x-x_0)^2}

    2. \displaystyle{|\overline{PQ}|=\sqrt{(x-x_0)^2+(y-y_0)^2}}

    Replace \displaystyle{(y-y_0)^2} by the term of #1:

    \displaystyle{|\overline{PQ}|=\sqrt{(x-x_0)^2+\frac1{m^2}(x-x_0)^2}}

    \displaystyle{|\overline{PQ}|=\sqrt{\frac{m^2}{m^2  } (x-x_0)^2+\frac1{m^2}(x-x_0)^2}}

    Factor out \displaystyle{(x-x_0)^2}

    \displaystyle{|\overline{PQ}|=\sqrt{\frac{m^2-1}{m^2} (x-x_0)^2}}
    Thanks from muddywaters
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  4. #4
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    Re: perpendicular lines

    yes. thanks
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