Question

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. based on this information, which pair of lines, together, could be perpendicular to rs? select two options.

Explanation:

Step1: Recall perpendicular - line and plane relationships

If a line is in a plane and the two planes are perpendicular, and another line lies in the intersection of the two planes, lines in the first - plane that are perpendicular to the intersection line are perpendicular to the line in the intersection.
Since planes \(X\) and \(Y\) are perpendicular and points \(R\) and \(S\) are in both planes, \(\overline{RS}\) lies on the intersection of planes \(X\) and \(Y\).
Lines in plane \(X\) that are perpendicular to the intersection line (i.e., \(\overline{RS}\)) are perpendicular to \(\overline{RS}\).
Lines \(\overline{EA}\) and \(\overline{FG}\) are in plane \(X\) and can be perpendicular to \(\overline{RS}\) (because they are in plane \(X\) and we can assume the appropriate orientation for perpendicularity based on the plane - plane perpendicularity).

Answer:

EA, FG