Results 1 to 7 of 7
  1. #1
    Bronze Lounger Maudibe's Avatar
    Join Date
    Aug 2010
    Location
    Pa, USA
    Posts
    1,213
    Thanks
    46
    Thanked 231 Times in 212 Posts

    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?
    Attached Images Attached Images
    Last edited by Maudibe; 2013-07-28 at 15:22. Reason: clarify per wisdom of the BATcher

  2. #2
    Super Moderator BATcher's Avatar
    Join Date
    Feb 2008
    Location
    A cultural area in SW England
    Posts
    2,833
    Thanks
    19
    Thanked 110 Times in 104 Posts
    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.
    BATcher

    Dear Diary, today the Hundred Years War started ...

  3. #3
    Bronze Lounger Maudibe's Avatar
    Join Date
    Aug 2010
    Location
    Pa, USA
    Posts
    1,213
    Thanks
    46
    Thanked 231 Times in 212 Posts
    Clarifications made using "y". Now if I can only stump the BATcher!

  4. #4
    Super Moderator BATcher's Avatar
    Join Date
    Feb 2008
    Location
    A cultural area in SW England
    Posts
    2,833
    Thanks
    19
    Thanked 110 Times in 104 Posts
    Another quite hard problem for a maths-rusty brain!

    BATcher

    Dear Diary, today the Hundred Years War started ...

  5. #5
    Bronze Lounger Maudibe's Avatar
    Join Date
    Aug 2010
    Location
    Pa, USA
    Posts
    1,213
    Thanks
    46
    Thanked 231 Times in 212 Posts
    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

  6. #6
    5 Star Lounger
    Join Date
    Jan 2001
    Location
    La Jolla,CA
    Posts
    1,091
    Thanks
    13
    Thanked 37 Times in 36 Posts
    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)

  7. #7
    Bronze Lounger Maudibe's Avatar
    Join Date
    Aug 2010
    Location
    Pa, USA
    Posts
    1,213
    Thanks
    46
    Thanked 231 Times in 212 Posts
    Done from a totally different angle (no pun intended). Brilliant KW!

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •