# <span lang="EN-US

Let A(-1, 0), B(3, 1), C(2, 2) and D(x, y) be the vertices of a parallelogram ABCD taken in order.

Since, the diagonals of a parallelogram bisect each other,

Coordinates of the mid-point of AC = Coordinates of the mid-point of BD As we know the coordinates of A and C both, we find the midpoint AC.

Midpoint of AC:

x- coordinate = (x1 + x2) / 2

= (-1 + 2 ) / 2 = 1/2

y-coordinate = (y1 + y2) / 2

= (0 + 2 ) / 2 = 1

Mid point of AC = ( 1/2 , 1)

As mid point of AC = mid point of BD

Mid point of BD = ( 1/2 , 1)

x- coordinate = (x1 + x2) / 2

= ( x + 3 ) / 2

(x + 3)/2 = 1/2
x + 3 = 1
x = -2

y- coordinate = (y1 + y2)/2

= (y + 1 ) / 2

(y + 1) /2 = 1
y + 1 =2
y=1

The coordinates of the fourth vertex, D are ( -2 , 1 ).

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