Question

Is the following statement always, sometimes, or never true? Through any three points, two points there is exactly one plane.

A: Always
B: Sometimes
C: Never
D: None

Answer 1

The statement is always true because three non-collinear points uniquely determine a plane.

Step-by-step explanation:

The statement is always true.

Through any three points in space, there is exactly one plane that contains those points. This is because three non-collinear points uniquely determine a plane. If we have two points, we can always find a third point not on the line formed by those two points, and these three points will determine a plane.

For example, imagine three points A, B, and C. We can draw a line connecting A and B. Then, we can draw a line connecting A and C that is not parallel to the line through A and B. These three non-collinear points define a plane, and any other point in space can be uniquely identified on this plane.