Planes X and Y are perpendicular. Points A, E, F, and G are points only in plane X. Points R and S are points in both planes X and Y. Lines EA and FG are parallel.

Question

Planes X and Y are shown. Lines A E and F G are vertical and are on plane X. Line R S is at the intersection of the 2 planes.
Based on this information, which pair of lines, together, could be perpendicular to RS? Select two options.

Line E A
Line E R
Line E F
Line F G
Line F S

Answer 1

To determine which pairs of lines could be perpendicular to line RS, we need to consider the relationships and orientations of the given lines.

1. Line EA: This line is vertical and lies completely within plane X.

2. Line FG: This line is also vertical and lies completely within plane X.

3. Line ER: This line connects points E (in plane X) to point R (which is in both planes X and Y). Given that point R lies on the intersection of the two planes, line ER could potentially be perpendicular to RS, depending on the spatial arrangement.

4. Line FS: Similarly, this line connects point F (in plane X) to point S (which also exists in both planes). Like ER, this line might also be perpendicular to RS depending on its orientation.

Given the descriptions:

• Lines EA and FG are parallel and in the same plane (plane X).
• Lines ER and FS connect points in plane X to points in plane Y (specifically at the intersection of the two planes).

Therefore, the lines that could be perpendicular to line RS (since RS is in the intersection of planes X and Y) would be:

• Line ER (because it connects point E in plane X to point R in both planes).
• Line FS (for the same reason as above).

In conclusion, the pairs of lines that could be perpendicular to RS are:

• Line E R
• Line F S