Final answer:
Based on geometric principles in three-dimensional space, we can confirm that statement B is true, as exactly one plane can contain any set of three non-collinear points. Statements A, C, and D cannot be definitively confirmed without more information on the relative positions of the points and planes mentioned.
Step-by-step explanation:
To address the question and determine the truth of the given statements, we need to apply our knowledge of geometry, specifically the properties of planes and lines in three-dimensional space. Let's analyze each statement:
A. There can actually be an infinite number of planes that contain three non-collinear points A, B, and C, so this statement is false.
B. There is indeed exactly one plane that contains any given set of three non-collinear points, in this case, E, F, and B, making this statement true.
C. If points C and G both lie in plane X, then the line drawn through them would also lie in that plane, so this statement could be true, depending on the placement of points C and G relative to plane X, which we do not have adequate information to determine.
D. Similar to statement C, if points E and F both lie in plane Y, any line drawn through them would lie in that plane as well, so this statement is potentially true depending on the actual positions of points E and F.
Without specific information about the positions of points C, G, E, and F in relation to planes X and Y, we cannot definitively determine the truth of statements C and D. Therefore, based on the given information and principles of geometry, the only statement we can confirm as true is statement B.