Three vertices of a parallelogram are A (-6, -7), B (-4, 5) and C (3, 1). What are the coordinates of the fourth vertex?

Three vertices of a parallelogram are A (-6, -7), B (-4, 5) and C (3, 1).
What are the coordinates of the fourth vertex?
The diagonals of a parallelogram bisect each other.
Use the midpoint formula to find the midpoint between points (x1, y1) and (x 2, y 2).
The formula is written as and is shown by:
(that is, the average of the x-coordinates and the average of the y-coordinates).
The mid-point of AC is (-1.5, -3).
The co-ordinates of the fourth vertex is D (1, -11).

Let D(x, y) be the coordinates of the fourth vertex.

Case I : Parallelogram ABCD
Coordinates of the point of intersection of diagonals AC and BD.
(-4 + x)/2 = (-6 + 3)/2 and (5 + y)/2 = (-7 + 1)/2
-4 + x = -6 + 3 and 5 + y = -7 + 1
x = 1 and y = -11
Hence, coordinates of the fourth vertex = (1, -11)

Case II : Parallelogram ABDC
Coordinates of the point of intersection of diagonals AD and BC.
(-6 + x)/2 = (-4 + 3)/2 and (-7 + y)/2 = (5 + 1)/2
-6 + x = -4 + 3 and -7 + y = 5 + 1
x = 5 and y = 13
Hence, coordinates of the fourth vertex = (5, 13)

Case III : Parallelogram ACBD
Coordinates of the point of intersection of diagonals AB and CD.
(3 + x)/2 = [-4 + (-6)]/2 and (1 + y)/2 = [5 + (-7)]/2
3 + x = -4 - 6 and 1 + y = 5 - 7
x = -13 and y = -3
Hence, coordinates of the fourth vertex = (-13, -3)

The sum of the coordinates at the ends of the diagonals is the same, so
.. A +C = B +D
.. D = A +C -B = (-6 +3 -(-4), -7 +1 -5)

D = (1, -11)

D(x,y)
It could be ABCD or ACBD
If ABCD then x-4=-6+3 and y+5=-7+1 , so D(1,-11)
If ACBD then ...