Question

critical thinking which situations are possible? point p is contained in exactly zero planes. point a is contained in an infinite number of planes. point x is contained in each of the parallel planes y and z. point h is contained in each of the intersecting planes j, k, and l. point q is contained in each of the perpendicular planes r and s.

Explanation:

Step1: Recall plane - point relationship

A point in 3 - D space is always in at least one plane. So, a point cannot be in exactly zero planes.

Step2: Consider a single point

A single point lies on an infinite number of planes. For example, rotate a plane around the point in 3 - D space.

Step3: Analyze parallel planes

Parallel planes do not intersect, so a point cannot be in two parallel planes simultaneously.

Step4: Analyze intersecting planes

The intersection of three planes can be a point. So a point can be in three intersecting planes.

Step5: Analyze perpendicular planes

The intersection of two perpendicular planes is a line, and a point on that line is in both planes.

Answer:

Point A is contained in an infinite number of planes.
Point H is contained in each of the intersecting planes J, K, and L.
Point Q is contained in each of the perpendicular planes R and S.