Question

planes a and b both intersect plane s. 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.

Explanation:

Step1: Check each option

• Option 1: Points \(N\) and \(K\) are on plane \(A\) and plane \(S\).
• From the diagram, points \(N\) and \(K\) lie on the intersection of plane \(A\) and plane \(S\). So this option is correct.
• Option 2: Points \(P\) and \(M\) are on plane \(B\) and plane \(S\).
• Point \(M\) is on plane \(B\) but not on plane \(S\). So this option is incorrect.
• Option 3: Point \(P\) is the intersection of line \(n\) and line \(g\).
• From the diagram, point \(P\) is the intersection of line \(n\) and line \(g\). So this option is correct.
• Option 4: Points \(M\), \(P\), and \(Q\) are non - collinear.
• Points \(M\), \(P\), and \(Q\) do not lie on the same straight line. So this option is correct.
• Option 5: Line \(d\) intersects plane \(A\) at point \(N\).
• Line \(d\) does not intersect plane \(A\) at point \(N\). So this option is incorrect.

Answer:

Points \(N\) and \(K\) are on plane \(A\) and plane \(S\), Point \(P\) is the intersection of line \(n\) and line \(g\), Points \(M\), \(P\), and \(Q\) are non - collinear.