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 plane - line relationship

A line is contained in a plane if all points on the line are in the plane.

Step2: Analyze each option

• Option 1: Point C is not in plane Y, so the line through C and D is not contained in plane Y.
• Option 2: Points D and E are both in plane Y. By the postulate that if two points lie in a plane, the line containing them lies in the plane, the line through D and E is contained in plane Y.
• Option 3: Points C and F can lie in plane X, not just point F.
• Option 4: Points D, E and other points in the intersection of the two - planes and other points in plane Y can lie in plane Y, not just D and E.

Answer:

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