How Many Different Parallograms Given 3 Points

[darkchild]

Homework Statement

This is a gre math subject test practice question: Consider the points A=(-1,2), B=(6,4), and C=(1,-20) in the plane. For how many different points D in the plane are A, B, C, and C the vertices of a parallelogram?

Homework Equations

none given

The Attempt at a Solution

I calculated one solution, D=(-6, -22), by figuring out what the coordinates had to be so that DC || AB and AD || BC. The answer sheet says that there are THREE different points. If someone could explain how this is even possible, I'd be much obliged.

 

[rummgamon]

there's also DA||BC

 

[epenguin]

The Attempt at a Solution

I calculated one solution, D=(-6, -22), by figuring out what the coordinates had to be so that DC || AB and AD || BC. The answer sheet says that there are THREE different points. If someone could explain how this is even possible, I'd be much obliged.

Seems calculation is long way round if question is just how many points?

Sketch and it turn take two sides as sides of parallelogram.