At least how many points determine exactly one plane?
The correct answer and explanation is:
At least three non-collinear points are required to determine exactly one plane.
A plane is a two-dimensional flat surface that extends infinitely in all directions. To define a unique plane, you need three points that are not all on the same line. This is because a single point or two points can be used to define a line, but to define a plane, you need more information. A plane requires three points that can be used to create vectors, and these vectors must not be parallel (i.e., the points must not be collinear).
When you have two non-collinear points, you can draw an infinite number of planes through those points. The addition of a third point, which is not on the same line, forces the plane to be unique because it locks the direction of the plane in space. The three points will create two vectors that are not parallel, and these vectors will determine the orientation of the plane.
In summary, while one point or two points can be used to define a line, a minimum of three points is necessary to uniquely define a plane. If these points are collinear, the situation would not determine a unique plane, as an infinite number of planes can pass through a straight line. The critical condition is that the three points must not lie on the same line, ensuring that they span a unique two-dimensional surface in three-dimensional space.