Geometry

Question Analysis
This question tests the ability to find the equation of the perpendicular bisector of a line segment. The key steps involve finding the midpoint of the segment and the slope of the line, then using the negative reciprocal of the slope to find the equation of the perpendicular bisector.

Key Concept Explanation
The perpendicular bisector of a line segment is a line that passes through the midpoint of the segment and is perpendicular to it. The slope of the perpendicular bisector is the negative reciprocal of the slope of the original line.

Step-by-step Solution
1. Find the midpoint of the segment with endpoints (1, 2) and (5, 6):
Midpoint = .
2. Calculate the slope of the segment:
Slope = .
3. Determine the slope of the perpendicular bisector:
The negative reciprocal of 1 is -1.
4. Use the point-slope form of the line equation with the midpoint (3, 4) and slope -1:

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