To solve this, let's define what the perpendicular bisector of a line is:

A perpendicular bisector of a line segment is a line that:

1. Intersects the line segment at its midpoint.
2. Is perpendicular (forms a 90-degree angle) to the line segment.

Now, reviewing the options:

• Option A: This is a diagonal line, not perpendicular to line XY.
• Option B: These are two parallel lines, not perpendicular or bisecting.
• Option C: This line intersects line XY perpendicularly at the midpoint, making it a potential correct option.
• Option D: This line is perpendicular, but it does not clearly bisect line XY.
• Option E: This is a diagonal line, neither perpendicular nor bisecting.
• Option F: The line intersects but is not perpendicular to XY.
• Option G: The line is horizontal and parallel, not perpendicular to XY.

The correct answer is Option C, as it shows a line perpendicular to XY and bisecting it at the midpoint.

Would you like more details on perpendicular bisectors or have any further questions?

Related Questions:

1. What are the properties of a perpendicular bisector in a triangle?
2. How do you find the equation of a perpendicular bisector given two points?
3. What is the geometric significance of the perpendicular bisector in circle construction?
4. Can a perpendicular bisector be extended infinitely, and how does that affect its properties?
5. How can perpendicular bisectors be used to find the center of a circle?

Tip: A perpendicular bisector always splits a line segment into two equal parts and forms right angles with it!