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: Analyze the first option

Points \(N\) and \(K\) are on plane \(A\) and plane \(S\). Looking at the diagram, point \(N\) is on both plane \(A\) and plane \(S\), but point \(K\) is only on plane \(A\) (not on plane \(S\)). So this option is false.

Step2: Analyze the second option

Points \(P\) and \(M\) are on plane \(B\) and plane \(S\). Point \(P\) is on both plane \(B\) and plane \(S\), and point \(M\) is on plane \(B\) and plane \(S\) (since line \(n\) (on which \(M\) lies) intersects plane \(S\) at \(P\) and \(M\) is on line \(n\) which is in plane \(B\)). So this option is true.

Step3: Analyze the third option

Point \(P\) is the intersection of line \(n\) and line \(g\). From the diagram, line \(n\) and line \(g\) intersect at point \(P\). So this option is true.

Step4: Analyze the fourth option

Points \(M\), \(P\), and \(Q\) are non - collinear. Non - collinear means the points do not lie on the same straight line. Looking at the diagram, points \(M\), \(P\), and \(Q\) do not lie on a single straight line. So this option is true.

Step5: Analyze the fifth option

Line \(d\) intersects plane \(A\) at point \(N\). Line \(d\) intersects plane \(A\) at point \(L\) (not \(N\)). So this option is false.

Answer:

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