If more than one plane contains three points A,B, and C, what must be true?

A)AB is perpendicular to BC
B)A,B, and C are noncollinear
C)A,B, and C are collinear
D)AB=BC

The correct answer is B) A, B, and C are noncollinear.

If more than one plane contains three points A, B, and C, it implies that the three points are not in a straight line, which means they are noncollinear. Collinear points lie on the same line, whereas noncollinear points do not. Therefore, option B) is the correct answer.

To determine what must be true if more than one plane contains three points A, B, and C, let's analyze the options:

A) AB is perpendicular to BC:
This statement does not necessarily need to be true. If AB is not perpendicular to BC, it does not indicate that more than one plane contains the three points.

B) A, B, and C are noncollinear:
This statement must be true. If more than one plane contains three points, it implies that the points are noncollinear. Collinear points lie on the same line, and if three points were collinear, they would only define one plane, not more.

C) A, B, and C are collinear:
This statement is not necessarily true. As discussed earlier, if more than one plane contains the three points, it indicates that the points are noncollinear.

D) AB = BC:
This statement does not need to be true. The lengths of AB and BC do not influence whether more than one plane can contain the points.

So, the correct answer is B) A, B, and C are noncollinear. This is the only option that must be true if more than one plane contains the three points.

Just use your right hand for one plane and your left hand for a second plane.

Intersect our flat right hand with your flat right hand.
They meet in a line.
All points that are in both planes lie on that line.