What is the correct method to write the equation of the perpendicular bisector of a line segment?

What is the correct method to write the equation of the perpendicular bisector of a line segment?

• A. Find the length of the segment
• B. Determine the midpoint and the slope of the opposite sides
• C. Calculate the distance between two endpoints
• D. Take the negative of the slope of the line

Answer: (B)

To write the equation of the perpendicular bisector of a line segment, determining the midpoint and the slope of the opposite sides is essential. First, you need to find the midpoint of the segment by averaging the coordinates of the endpoints, which provides the point through which the perpendicular bisector will pass. Next, calculating the slope of the original line segment allows you to understand the orientation of the segment itself. The perpendicular bisector will have a slope that is the negative reciprocal of the slope of the segment. This negative reciprocal property is crucial because it ensures that the two lines are perpendicular to each other. Once you have the midpoint and the slope of the perpendicular bisector, you can then use the point-slope formula to write the equation. Therefore, option B encompasses both critical steps needed for correctly finding the equation of the perpendicular bisector: locating the midpoint and determining how the slope relates to perpendicularity.

To write the equation of the perpendicular bisector of a line segment, determining the midpoint and the slope of the opposite sides is essential. First, you need to find the midpoint of the segment by averaging the coordinates of the endpoints, which provides the point through which the perpendicular bisector will pass.

Next, calculating the slope of the original line segment allows you to understand the orientation of the segment itself. The perpendicular bisector will have a slope that is the negative reciprocal of the slope of the segment. This negative reciprocal property is crucial because it ensures that the two lines are perpendicular to each other.

Once you have the midpoint and the slope of the perpendicular bisector, you can then use the point-slope formula to write the equation. Therefore, option B encompasses both critical steps needed for correctly finding the equation of the perpendicular bisector: locating the midpoint and determining how the slope relates to perpendicularity.