Final answer:
The correct answer is C) n, as lines that are perpendicular to the same line are parallel to each other in a plane.
Step-by-step explanation:
The question involves understanding the relationships between slopes of parallel and perpendicular lines in Cartesian geometry. In a plane, lines that are perpendicular to the same line are parallel to each other. If line f is perpendicular to line m, and another line is also perpendicular to m, then it follows that line f must be parallel to this other line.
The question contains a missing term, represented by a blank, and the correct option should express the line that is perpendicular to line m and thus parallel to line f. The statement, therefore, should read: "In a plane, if line f is perpendicular to line m and line n is also perpendicular to line m, then f ∥ n."This is a direct consequence of the geometric fact that perpendicular lines to the same line are parallel to each other.