**closed**

###### Answers:

Follow the following steps to work out with this problem:-

First draw the parallelogram with AB//CD and AD//BC.

Draw the diagonals AC and BD to intersect at O.

We know that diagonals of a parallelogram bisect each other at the point of intersection.

Therefore O is the midpoint of AC and BD.

Now find the co-ordinates of the point O by applying section formula on the diagonals AC (ratio in which O divides AC and BD is 1:1)

The co-ordinates come out to be O[(x1+x3)/2],[(y1+y3)/2].

Let us assume that co-ordinates of D is D(a,b).

Apply section formula on line segment BD and again find the co-ordinates of point O.

(Ratio is 1:1).

The co-ordinates come out to be O[(x2+a)/2],[(y2+b)/2].

Since the co-ordinates are of the same point O, they are equal.

Therefore,

O[(x1+x3)/2],[(y1+y3)/2]=O[(x2+a)/2],[(y2+b)/2]

Equate x coordinate and y coordinate separately.

The answer that follows is

D(a,b)=D(x1+x3-x2 , y1+y3-y2).