Question

planes x and y and points c, d, e, and f are shown which statement is true about the points and planes? the line that can be drawn through points c and d is contained in plane y the line that can be drawn through points d and e is contained in plane y the only point that can lie in plane x is point f the only points that can lie in plane y are points d and e

Explanation:

Step1: Recall the property of a plane

A plane contains all the points that lie on it. If two points lie on a plane, then the line passing through them lies on that plane.

Step2: Analyze each option

• For the line through C and D: Point C is not on plane Y, so the line through C and D is not contained in plane Y.
• For the line through D and E: Both D and E are on plane Y. By the property of a plane (if two points \(P\) and \(Q\) are on a plane \(\alpha\), then the line \(\overleftrightarrow{PQ}\) is on \(\alpha\)), the line through D and E is contained in plane Y.
• For the statement about point F: There is no information to suggest that only point F can lie in plane X. Other points (not shown in the limited - given set \(C,D,E,F\)) could also lie in plane X.
• For the statement about plane Y: Points D and E are on plane Y, but there could be other points (not in the set \(C,D,E,F\)) on plane Y as well. A plane has infinitely many points.

Answer:

The line that can be drawn through points D and E is contained in plane Y.