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  1. #1
    Bronze Lounger Maudibe's Avatar
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    What's the Point?

    Points A, B and C are defined by their coordinates in a standard rectangular system of axes. What positive value of y in point B makes triangle ABC a right triangle with AC its hypotenuse?
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    Last edited by Maudibe; 2013-07-28 at 15:22. Reason: clarify per wisdom of the BATcher

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  3. #2
    Super Moderator BATcher's Avatar
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    Afraid it will have to wait until tomorrow, since I have to get up at 05:15 GMT.

    But you might like to change the diagram so that the coordinates of B are (4,b)?!
    Last edited by BATcher; 2013-07-28 at 14:40.
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  4. #3
    Bronze Lounger Maudibe's Avatar
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    Clarifications made using "y". Now if I can only stump the BATcher!

  5. #4
    Super Moderator BATcher's Avatar
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    Another quite hard problem for a maths-rusty brain!

    BATcher

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  6. #5
    Bronze Lounger Maudibe's Avatar
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    Damn, you are good! BTW, you can produce a square root symbol in an Excel cell using the Symbol menu on the Insert Tab. Then do a copy/paste: √1000

  7. #6
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    Explanation:

    In order to make AB perpendicular to BC (to form the right triangle), the slopes of AB and BC must be negative reciprocals of each other.

    So, (y-1)/3 must equal the neg recip of (y-1)/-2 or

    (y-1)/3 = 2/(y-1).

    Then, "cross multiply" and get: y^2 - 2y + 1 = 6 and y^2 - 2y - 5 = 0.

    Using the quadratic formula: [2 + SQRT(4+20)]/2 which is [2 + sqrt(24)]/2 which is [2+2sqrt(6)]/2

    So, the answer is: 1+sqrt(6)

  8. #7
    Bronze Lounger Maudibe's Avatar
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    Done from a totally different angle (no pun intended). Brilliant KW!

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