Question
Planes A and B both intersect plane S.
Vertical plane S intersects horizontal plane A and horizontal plane B. Plane S and plane A intersect at line f. Line f contains points N and K. Plane S and plane B intersect at line g. Line g contains points P and Q. Line d intersects plane A at point L.
Which statements are true based on the diagram? Select three options.
Points N and K are on plane A and plane S.
Points P and M are on plane B and plane S.
Point P is the intersection of line n and line g.
Points M, P, and Q are noncollinear.
Line d intersects plane A at point N.
Vertical plane S intersects horizontal plane A and horizontal plane B. Plane S and plane A intersect at line f. Line f contains points N and K. Plane S and plane B intersect at line g. Line g contains points P and Q. Line d intersects plane A at point L.
Which statements are true based on the diagram? Select three options.
Points N and K are on plane A and plane S.
Points P and M are on plane B and plane S.
Point P is the intersection of line n and line g.
Points M, P, and Q are noncollinear.
Line d intersects plane A at point N.
Answers
GPT-4o mini
To determine which statements are true based on the provided information about planes and lines, we can analyze each statement:
1. **Points N and K are on plane A and plane S.**
- True. Line f, which is the intersection of plane S and plane A, contains points N and K. This means both points are located on both plane A and plane S.
2. **Points P and M are on plane B and plane S.**
- False. While point P is on line g, which is the intersection of plane B and plane S, there is no information provided about point M to indicate it lies on plane B or plane S.
3. **Point P is the intersection of line n and line g.**
- False. No information has been provided about line n, so we cannot conclude that point P is the intersection of line n and line g.
4. **Points M, P, and Q are noncollinear.**
- This statement cannot be evaluated based on the given information. We don't have data about point M's location relative to points P and Q, so we cannot determine if they are collinear or not.
5. **Line d intersects plane A at point N.**
- False. The provided information states that line d intersects plane A at point L, not point N.
Based on this analysis, the three true statements from your options are:
- Points N and K are on plane A and plane S.
***Note**: You only provided one statement that is definitely true. If there are additional statements or options, please clarify to receive a more thorough analysis.*
1. **Points N and K are on plane A and plane S.**
- True. Line f, which is the intersection of plane S and plane A, contains points N and K. This means both points are located on both plane A and plane S.
2. **Points P and M are on plane B and plane S.**
- False. While point P is on line g, which is the intersection of plane B and plane S, there is no information provided about point M to indicate it lies on plane B or plane S.
3. **Point P is the intersection of line n and line g.**
- False. No information has been provided about line n, so we cannot conclude that point P is the intersection of line n and line g.
4. **Points M, P, and Q are noncollinear.**
- This statement cannot be evaluated based on the given information. We don't have data about point M's location relative to points P and Q, so we cannot determine if they are collinear or not.
5. **Line d intersects plane A at point N.**
- False. The provided information states that line d intersects plane A at point L, not point N.
Based on this analysis, the three true statements from your options are:
- Points N and K are on plane A and plane S.
***Note**: You only provided one statement that is definitely true. If there are additional statements or options, please clarify to receive a more thorough analysis.*