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Question

Show that the points A(3, 3, 3), B(0, 6, 3), C(1, 7, 7) and D(4, 4, 7)


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    Solution

    AB=(03)2+(63)2+(33)2

    =(3)2+(3)2+(0)2=9+9

    =32 units

    BC=(10)2+(76)2+(73)2

    =(1)2+(1)2+(4)2

    =1+1+16=32 units

    AC=(13)2+(73)2+(73)2

    =(2)2+(4)2+(4)2

    =4+16+16=36 =6 units

    BD =(40)2+(46)2+(73)2

    = (4)2+(2)2+(4)2

    =16+4+16=36=6 units

    CD = (41)2+(47)2+(77)2

    =(3)2+(3)2+(0)2

    =9+9

    =32 units

    AD=(43)2+(43)2+(73)2

    =(1)+(1)2+(4)2=1+1+16

    =32 units

    Since,

    AB = BC = CD = DA

    And AC = BD

    Since, all sides and diagnols of quadrilateral ABCD all equal.


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