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Math Help - Circumcenter and Orthocenter of a triangle

  1. #16
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    Here's the orthocentre, roughly.

    You wrote y=22.78 instead of -22.78 for this.
    Attached Thumbnails Attached Thumbnails Circumcenter and Orthocenter of a triangle-orthocenrtre.jpg  
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  2. #17
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    thank you so much for this
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  3. #18
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    Quote Originally Posted by Archie Meade View Post
    Here's the orthocentre, roughly.

    You wrote y=22.78 instead of -22.78 for this.
    the point on the picture is like (51,-18), it doesnt match with my calculations, can u explain how to do it the right way? if it's not too much trouble? thx
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  4. #19
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    You had earlier, the equation y=-\frac{21}{6}x+150.5

    For x=49.5, this is -21(8.2)+150.5=-172.2+150.5=-21.7 approx

    My diagram is not carefully done,
    it looks like y is about -18, but it would be correct, if i'd taken more time to draw a very accurate sketch.
    Attached Thumbnails Attached Thumbnails Circumcenter and Orthocenter of a triangle-orthocentre1.jpg  
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  5. #20
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    To verify your calculations, place the co-ordinates of the orthocentre into the equations of the perpendicular lines.
    The orthocentre is a point on both of the perpendiculars, which contain the opposite vertex (actually all 3 perpendiculars).

    If you calculate the orthocentre correctly,
    which you did except for having the sign on the y co-ordinate wrong,
    you should now be able to place x=49.5 into both y=-\frac{21}{6}x+150.5 and y=20x-1013

    and get the exact same y=-22 approx for both.

    Or you could use y and find that you get the same x=49.5 for both
    (or all 3 perpendiculars, if you formulate the 3rd one).
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  6. #21
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    Quote Originally Posted by Archie Meade View Post
    To verify your calculations, place the co-ordinates of the orthocentre into the equations of the perpendicular lines.
    The orthocentre is a point on both of the perpendiculars, which contain the opposite vertex (actually all 3 perpendiculars).

    If you calculate the orthocentre correctly,
    which you did except for having the sign on the y co-ordinate wrong,
    you should now be able to place x=49.5 into both y=-\frac{21}{6}x+150.5 and y=20x-1013

    and get the exact same y=-22 approx for both.

    Or you could use y and find that you get the same x=49.5 for both
    (or all 3 perpendiculars, if you formulate the 3rd one).
    thanks you so much, i think i get it now.
    ima try to draw it myself
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  7. #22
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    When you draw hand sketches, normally the co-ordinates will be a little bit
    off, since you'd have to draw extremely accurately.

    Solving the equations is very exact, though it's best to write
    the x and y co-ordinates of the centres as fractions rather than decimals.

    Practice and you'll improve fast.
    Circumcentre and orthocentre are good for mastering line equations.
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