Question 1203482: the three vertices of a parallelogram are (1,3);(0,0);(4,0) Find the three possible locations of the fourth vortex
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! the three vertices of a parallelogram are
( , )
( ,)
( ,)
Find the three possible locations of the fourth vortex
a parallelogram is a figure with opposite sides parallel
the fourth vortex is ( , )
line that passes through ( ,) and (,) is parallel to line that passes through (,) and ( , )
so, find a slope of the line that passes through (,) and (,) :
parallel lines have same slope, so line that passes through ( ) and ( ,) will be
 ..use point (,)
now, we know that point ( , ) will be intersection of tis line and a line that passes through ( , ) and is parallel to x-axis, or a line 
and
(,) = ( ,)
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
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.
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