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 x. 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 - point relationship

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

Step2: Analyze each option

• Option 1: Points C and D. Point C is in plane \(x\) and point D is in plane \(y\). The line through C and D is not contained in plane \(y\) since C is not in plane \(y\).
• Option 2: Points D and E. Both D and E are in plane \(y\). By the property that if two points lie in a plane, the line passing through them lies in the same plane, the line that can be drawn through points D and E is contained in plane \(y\).
• Option 3: Points C, D, E, and F are shown. Point C also lies in plane \(x\), so it's not true that only point F can lie in plane \(x\).
• Option 4: Point F also lies in plane \(y\), so it's not true that only points D and E can lie in plane \(y\).

Answer:

The line that can be drawn through points D and E is contained in plane \(y\).