Parallelograms are a type of polygons
which you can apply
the vectors to calculate some of their
elements (vertexes, sides, diagonals, midpoints,...)
knowing others. For instance:
1) From
one parallelogram
ABCD give us three consecutive vertexes D,
A and B, and it is asked the other vertex C,
we can calculate it making one of the translations:
C
= D +
=
D + ![](gif/xvec_ab.gif)
C
= B +
=
B + ![](gif/xvec_ad.gif)
where we
have used the fact that
=
and
=
,
they make ABCD a parallelogram (we remember that
=BA
and
=DA).
2) Also in
the same previous conditions, that is to say, known three
consecutive vertexes D, A and B,
we can get the centre M of the parallelogram
(that it is also the intersection of the diagonals)
like midpoint of the segment BD, and later get C
like a symmetrical of A respect to C.
3) From a parallelogram
ABCD give us two consecutive vertexes A
and B, and his centre M, we can get the other
two vertexes C and D like symmetrical respective
to A and to B respect to M.