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the three vertices of a parallelogram are (1,3);(0,0);(4,0) Find the three possible locations of the fourth vertex.
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Surely, in this problem the major step and the major part
is to guess dispositions of these three parallelograms
and represent them. It is done in Figures 1, 2 and 3 below.
The 4th vertex is shown by red circle in each Figure, together with its coordinates.
As soon as the parallelograms are shown and presented, finding
the coordinates of the added 4th vertex is just a boring routine elementary procedure.
Figure 1. Fourth vertex is (5,3)
Figure 2. Fourth vertex is (-3,3)
Figure 3. Fourth vertex is (3,-3)
Solved and answered in full, with illustrations.