132k views
3 votes
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

User Alecwhardy
by
7.9k points

1 Answer

5 votes

Final answer:

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.

User Matt Morrison
by
9.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories