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The question is

Three vertices of a parallelogram ABCD are A(3,-1,2), B(1,2,-4) and C(-1,1,2). Find the coordinate of the fourth vertex.

To get the answer I tried the distance formula, equated AB=CD and AC=BD.

  • 0
    Doesn't this have more than one solution, depending on the order of the vertices in the parallelogram or is D meant to be connected to A and C?2012-12-19
  • 0
    A upper left, B upper right, C lower right, D lower left.2012-12-19
  • 0
    $AC$ and $BD$ must have the same mid point. The mid point of $AC$ is $(1,0,2)$ and hence $D$ is $(1, -2, 8)$2016-08-09

3 Answers 3