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Math Help - co-ordinates of a parallelogram

  1. #1
    Senior Member euclid2's Avatar
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    co-ordinates of a parallelogram

    ABCD is a parallelogram where A is (4,2), B is (-6,1), and D is (-3,-4). Find the co-ordinates of C.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    If you have a sketch, that should be simpler.

    The properties of a parallelogram is such that the sides AB and CD are parallel, meaning that AB and CD have the same gradient.
    Same for BC and AD; they have the same gradient.

    So:
    1. Find the gradient of AB. (this is also gradient of CD)
    2. Find the gradient of AD. (this is also gradient of BC)
    3. Find equation of line through D having gradient AB.
    4. Find equation of line through B having gradient AD.
    5. Solve simultaneously for those two lines. The intersection is where point C is.

    There is a shorter, visual way using vectors, but this makes a diagram a must, if you cannot picture the points in your head.

    Vector AB = (10, 1)
    So, C + (10, 1) = (-3, -4)
    So, C = (-3 -10, -4 -1) = (-13, -5)
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  3. #3
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    Hello, euclid2!

    If you make a sketch, you can "walk" your way to the answer.



    ABCD\text{ is a parallelogram with vertices: }A(4,2),\;B(\text{-}6,1),\;D(\text{-}3,\text{-}4)
    \text{Find the coordinates of }C.
    Code:
                                  A
                  B               o(4,2)
            (-6,1)o               :
                  :               : 
                  :               : -6
                  :               :
                  :       D   -7  :
          C       :       o - - - +
          o - - - +    (-3,-4)

    We see that vertex \,C is at the lower-left.

    Going from \,A to \,D, we move: 6 units down and 7 units left.

    Since BC \parallel AD, going from \,B to \,C, we do the same.


    Starting at B(\text{-}6,1), move 6 units down a 7 units left.

    Therefore, vertex \,C is (\text{-}13,\text{-}5)
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  4. #4
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    Quote Originally Posted by euclid2 View Post
    ABCD is a parallelogram where A is (4,2), B is (-6,1), and D is (-3,-4). Find the co-ordinates of C.
    B(-6 , 1) , A(4 , 2)
    C(a , b) , D(-3 , -4)

    4 - (-6) = -3 - a
    10 = -3 - a ===> a = -13

    2 - 1 = -4 - b
    1 = -4 -b ===> b = -5

    therefore C(-13 , -5)
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