Final answer:
The student's question pertains to geometry and the relationship between points and planes in a three-dimensional Cartesian coordinate system. Without a provided diagram, one can deduce that if points D and E lie on plane Y, the line through them is also in plane Y, making option (D) a likely answer.
Step-by-step explanation:
The student is asking about the relationship between points and planes in a geometric context, specifically in a three-dimensional Cartesian coordinate system where points are described by coordinates and vectors are broken down into x-components and y-components. The Cartesian system easily illustrates concepts like vector addition and the orthogonality of axes. Given points C, D, E, and F in relation to planes X and Y, without a diagram, we cannot definitively answer which statements are true about the points and planes. However, we can say that if points D and E both lie on plane Y, then the line drawn through them would also be contained in plane Y, making option (D) likely. This assumes that there are no additional contextual details that contradict this statement, such as the points lying on different regions of the plane.
In the context of Cartesian coordinates, understanding the positioning of points and lines in relation to planes is crucial for visualizing and solving geometric and vector problems geometric context, Cartesian coordinate system, and vector addition.