choices 2, 4, 5 are appropriate
Step-by-step explanation:
How to read the diagram
It can take a bit of practice to learn to interpret a diagram like this. A shaded parallelogram represents a plane. The planes each have a script capital letter identifying it. R, S, T.
Lines are shown with arrows on both ends. Those each have a lower-case letter identifier. The lines are identified as v, x, y, z. The points in the figure are solid black dots with an upper-case sans-serif letter identifier. The points are A, B, C, D, E. When the point is within the boundaries of the parallelogram representing a plane, it is considered to be in that plane.
You will notice that point A is in planes R and T, and is on lines v and y. Similarly, point B is in planes S and T, and is on lines v and x. The location of lines x and y shows those lines represent the lines of intersection of planes Sand T, and R and T, respectively. Since points A and B are both in plane T, line v through those points is also in that plane.
The dashed portion of line z indicates that portion of the line is "behind" plane S. Line z intersects plane S at point C, and extends through that plane to point D, which is not on any of the planes in the diagram. The fact that the arrowheads of line z are not inside any parallelogram is further clue that line z is not contained in any plane in this diagram.
How to choose the answers
1. As we said, point B is in planes S and T. Point E is in plane R. Plane S does not contain point E.
2. The line containing points A and B is line v. It lies entirely within plane T.
3. Line v intersects line x at point B. It intersect line y at point A. Points A and B are distinct points, so line v does not intersect lines x and y at the same point.
4. Point C is in plane S and on line z, which goes through the plane. Line z intersects plane S at point C.
5. Line y is shown as being in both planes R and T. Planes R and T intersect at line y.
