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