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Coordinates of the fourth vertex of a parallelogram

Posted July 13th, 2010 by Structure

Let $ A(x_1,y_1),B(x_2,y_2),C(x_3,y_3)\:and D(x,y) $ such as ABCD is a parallelogram.As AC and BD has the same middle point we have

$$x+x_2=x_1+x_3$$
$$y+y_2=y_1+y_3$$

So

$$x=x_1+x_3-x_2$$
$$y=y_1+y_3-y_2$$

So D has coordinates $ D(x_1+x_3-x_2,y_1+y_3-y_2). $

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