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How do I find the other corners of this square?

  1. Aug 8, 2010 #1
    [PLAIN]http://img713.imageshack.us/img713/6686/wtfhalp.jpg [Broken]

    How do I work out points B and D with only points A and C given? B and D have the same z-coordinates. I worked out the red vector, but have no idea what to do from there.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Aug 8, 2010 #2

    ehild

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    What do you know about the intersection of the diagonals?

    ehild
     
  4. Aug 8, 2010 #3
    They're perpendicular. I don't know how the dot product can help in this situation.
     
  5. Aug 8, 2010 #4

    ehild

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    I mean the point of intersection. Can you calculate its coordinates?

    ehild
     
  6. Aug 8, 2010 #5
    I would assume the point of intersection is half of AC which is (5.53615,-13.13056,4.176025)
     
  7. Aug 8, 2010 #6

    ehild

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    And also half of DB, isn't it?

    ehild
     
  8. Aug 8, 2010 #7
    Yes, but how do I go about finding the coordinates of D and B with it?
     
  9. Aug 8, 2010 #8

    ehild

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    The intersection of the diagonals is a point of the line DB. Both D and B have the same z coordinates, what is this coordinate?
    I you know the z coordinate of B, you can find two more equations to find the x and y coordinates.
    You know how far B is from the centre... you know that the diagonals are normal to each other. And both D and B are at equal distance from A and C...or the vectors AC and AB enclose a 45° angle ...


    ehild
     
  10. Aug 8, 2010 #9
    So I use pythagoras to find the length of AB and from there use the dot product to find the coordinates of B?
     
  11. Aug 8, 2010 #10

    ehild

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    Go ahead. Let me see what you do.

    ehild
     
  12. Aug 8, 2010 #11
    It did not work at all.
     
  13. Aug 8, 2010 #12

    ehild

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    I see. Won't you try?

    ehild
     
  14. Aug 8, 2010 #13
    Try what? I'm not sure what to do to get the equations for the x and y coordinates.
     
  15. Aug 8, 2010 #14

    thrill3rnit3

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    Diagonals of a square are congruent, and they intersect at their midpoints. You can Pythagoras' from there.
     
  16. Aug 8, 2010 #15
    I got the length, but how do I get the x and y coordinates of AB with it? Using the dot product doesn't really help.
     
  17. Aug 8, 2010 #16

    thrill3rnit3

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    Use the distance formula again. You have the coordinates of A, the length of AB, so you should be able to find the coordinates of B.
     
  18. Aug 9, 2010 #17
    But how?
     
  19. Aug 10, 2010 #18
    [PLAIN]http://img291.imageshack.us/img291/2650/62843747.jpg [Broken]

    That's all I can do. How do I use those distances to find x and y? I know to use pythagoras, but what am I using for a, b and c?
     
    Last edited by a moderator: May 4, 2017
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