Question 1205432
.
Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(4,5)
(1,-4)
(9,-6)
~~~~~~~~~~~~~~~~


<pre>
With 3 (three) given points as verices of a parallelogram, there are 3 possible options 
for the fourth vertex.


The algorithm of finding this 4-th vertex coordinates is as follows:


    (1) you take two vertices {{{P[1]}}} = ({{{x[1]}}},{{{y[1]}}}) and {{{P[2]}}} = ({{{x[2]}}},{{{y[2]}}})
        by an arbitrary way from the given three vertices.


    (2) you calculate the coordinates of the middle point between the selected points {{{P[1]}}} and {{{P[2]}}}

        {{{P[0]}}} = ({{{x[0]}}},{{{y[0]}}}) = ({{{(x[1]+x[2])/2}}},{{{(y[1]+y[2])/2}}})


    (3) finally, you calculate the coordinates of the 4-th vertex as

           {{{P[4]}}} = ({{{x[4]}}},{{{y[4]}}}) = ({{{x[0]+(x[0]-x[3])}}},{{{y[0]+(y[0]-y[3])}}}).
</pre>

That's all.