Let A(3,2) and B(-1,0) be the two vertices of the parallelogram ABCD.

Let M(2,-5) be the point where diagonals meet.

Since the diagonals of the parallelogram bisect each other, M is the midpoint of AC and BD.

Consider A-M-C

Let co-ordinate of C be (x₂,y₂)

x₁ = 3, y₁ = 2

x = 2, y = -5

By midpoint formula, x = (x₁+x₂)/2

2 = (3+x₂)/2

3+x₂ = 4

x₂ = 4-3 = 1

By midpoint formula, y = (x₁+x₂)/2

-5 = (2+y₂)/2

-10 = 2+y₂

y₂ = -10-2 = -12

Hence the co-ordinates of the point C are (1,-12).

Consider B-M-D

Let co-ordinate of D be (x₂,y₂)

x₁ = -1, y₁ = 0

x = 2, y = -5

By midpoint formula, x = (x₁+x₂)/2

2 = (-1+x₂)/2

-1+x₂ = 4

x₂ = 4+1 = 5

By midpoint formula, y = (x₁+x₂)/2

-5 = (0+y₂)/2

-10 = 0+y₂

y₂ = -10

Hence the co-ordinates of the point D are (5,-10).