How many parallelograms can be made by taking three points not on the same line as three vertices?

How many parallelograms can be made by taking three points not on the same line as three vertices?

3

If three points a, B and C are not collinear on the same plane, the parallelograms with their vertices share ()
A. 1 B. 2 C. 3 d. 4

As shown in the figure, connect three points a, B and C, take AB, BC and AC as parallelogram, diagonal as parallelogram, and make three parallelogram: ▱ ABCD, ▱ aceb and ▱ acbf, so select C

As shown in the figure, in the plane rectangular coordinate system, the midpoint a (4,0), point B (- 1 / 2,0) and point C (0,3) draw a parallelogram with a / B / C as the vertex to find the fourth vertex
Coordinates of points

There are three such points:
(1) AB and DC are opposite sides, which are parallel and equal
So the method of moving a to B is the same as that of moving d to C
A（4,0）、B（-1/2,0）
You can see that a to B move 9 / 2 units to the left
So D to C also moves 9 / 2 units to the left, so the coordinates of point D are (9 / 2,3)
(2) AB and CD are opposite sides
A to B move 9 / 2 units to the left, so C to d also move 9 / 2 units to the left
So the D coordinate is (- 9 / 2,3)
(3) AC and DB are opposite sides (AC and BD are opposite sides, the same as (2))
A to C move 4 units to the left and 3 units up
So D to B also move 4 units to the left and 3 units up
So the coordinates of point D are (7 / 2, - 3)

In the plane rectangular coordinate system, the points a, B and C are (0,0), (- 4,0), (- 3,2) respectively. If the parallelogram is drawn with ABC three points as the vertex, the fourth vertex cannot be drawn

The fourth vertex may be (1,2), (- 7,2) (- 1, - 2)
The fourth point is not to look at the topic by yourself