Question

line m intersects plane r at a single point. a) diagram of line m passing through plane r b) diagram of line m intersecting another line and labeled with r and m

Explanation:

Step1: Analyze Option A

In figure A, line \( m \) is shown as lying within plane \( R \) (since it's a dashed - solid line through the plane), so it does not intersect the plane at a single point. It is either on the plane (if the line is entirely within the plane) or parallel? No, here it's on the plane. So the statement "Line \( m \) intersects plane \( R \) at a single point" is false for A.

Step2: Analyze Option B

In figure B, line \( m \) and the other line (representing the plane? Wait, no, the plane - like figure? Wait, no, in figure B, line \( m \) and the vertical line (maybe representing the plane's edge? No, actually, in the diagram for B, line \( m \) and the other line cross at a point, and line \( m \) is not on the plane (unlike A where line \( m \) is through the plane). Wait, no, re - examining: The question is whether line \( m \) intersects plane \( R \) at a single point. In figure B, line \( m \) is a line that is not lying on the plane (unlike A where line \( m \) is within the plane's representation) and intersects the plane (the area around the other line) at a single point. Wait, maybe I misanalyzed A. Wait, in A, the plane \( R \) is the blue rectangle, and line \( m \) is a line that goes through the plane (the dashed part is inside, solid outside? No, the line in A is horizontal through the blue rectangle, so it is lying on the plane (a line on a plane intersects the plane at infinitely many points, not a single point). In B, the line \( m \) and the other line (maybe the plane's line) intersect at a point, and line \( m \) is not on the plane, so it intersects the plane at a single point. So the correct figure is B.

Answer:

B) (the option with the diagram where line \( m \) intersects the plane - related line at a single point, not lying on the plane like in A)