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Math Help - orthocenter

  1. #1
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    Smile orthocenter

    i need to find the orthocenter of a triangle
    the cooridinates are:
    X = 55, 51
    Y= 10 , 4
    Z = 49, 95

    and if you can, can you show work


    Thank You very much for your help
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Orthocentre

    Hello misterriceman
    Quote Originally Posted by misterriceman View Post
    i need to find the orthocenter of a triangle
    the cooridinates are:
    X = 55, 51
    Y= 10 , 4
    Z = 49, 95

    and if you can, can you show work


    Thank You very much for your help
    Suppose that the orthocentre, O, has coordinates (a, b). Then we use the fact that the line joining the orthocentre to any vertex is perpendicular to the opposite side. So:

    Gradient of OX = \frac{b-51}{a-55}

    Gradient of YZ = \frac{91}{39}

    So the product of these gradients is -1; i.e.

    \frac{91}{39}\times\frac{b-51}{a-55}= -1 (1)

    In a similar way, using OZ and XY, we get:

    \frac{47}{45}\times\frac{b-95}{a-49} = -1 (2)

    Now solve the simultaneous equations (1) and (2) to find a and b. (Horrible numbers!) I make this:

    a = \frac{382}{3} and b = 20

    I think you should check my working!

    Grandad
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  3. #3
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    thank u very muchhh
    i love u <3333333
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