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Math Help - Help me with a coordinate question

  1. #1
    Member helloying's Avatar
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    Help me with a coordinate question

    A(0,6) B(2,1) C(7,3) are the 3 possible vertices of a square. Find the coordinate of D, the fouth vertex of the square.
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  2. #2
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    You can find the gradients of the lines AB and BC, get the equations of DC and AD, and then solve the two line equations simultaneously to get the coordinates of D.

    I hope that helps.

    ILoveMaths07.
    Last edited by ILoveMaths07; September 19th 2008 at 12:42 AM.
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  3. #3
    Super Member 11rdc11's Avatar
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    D is (5,8) There is two ways i can think to solve this problem. 1 way is to use midpoints and the other way is to find the slope of AB and BC and use that info to find the equation of line AD and the equation of line CD. After that equal equation AD and CD to see where they intersect and that will be point D.
    Last edited by 11rdc11; September 19th 2008 at 12:58 AM. Reason: make answer clearer
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  4. #4
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    Oh, there's an easier way... Consider all the points as position vectors.

     \vec {OA} = 6\vec {j}
     \vec {OB} = 2\vec {i} + \vec {j}
     \vec {OC} = 7\vec {i} + 3 \vec {j}

    Then,  \vec {BC} = \vec {OC} - \vec {OB}
    \Rightarrow \vec {BC} = (7\vec{i} + 3 \vec {j}) - (2\vec {i} + \vec {j}) = 5\vec{i} + 2\vec{j}.

    Therefore, \vec {OD} - \vec {OA}, or \vec{AD}, will also equal  5\vec {i} + 2 \vec {j} (Because BC = AD; ABCD is a square)

    So \vec {OD} = \vec{OA} + 5 \vec {i} + 2\vec {j} = 6\vec{j} + 5 \vec {i} + 2\vec {j} = 5 \vec {i} + 8 \vec {j}. .

    So the coordinates of D are (5, 8).

    I hope that helps.

    ILoveMaths07.
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  5. #5
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    Quote Originally Posted by helloying View Post
    A(0,6) B(2,1) C(7,3) are the 3 possible vertices of a square. Find the coordinate of D, the fouth vertex of the square.
    Use vectors:

    \overrightarrow{OB} = (2,1)

    and:

    \overrightarrow{BA} = (-2,5)

    \overrightarrow{BC} = (5, 2)

    then

    \overrightarrow{OD} = \overrightarrow{OB} + \overrightarrow{BA} + \overrightarrow{BC} = (2,1) + (-2,5) + (5,2) = (5,8)
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  6. #6
    Super Member 11rdc11's Avatar
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    Another way you could solve this is by using the distance formula. Let me see if i can post a graph to explain what I mean clearer.
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