How to Find the Perpendicular Bisector of a Line Segment | Steps and Equation Simplification

Perpendicular Bisector

The perpendicular bisector is a line or a segment that cuts another line segment into two equal parts at a right angle

The perpendicular bisector is a line or a segment that cuts another line segment into two equal parts at a right angle. In simple terms, it is a line that passes through the midpoint of a given line segment and is perpendicular to that line segment.

To find the perpendicular bisector of a line segment, you can follow these steps:

1. Determine the midpoint of the given line segment by finding the average of the coordinates of its endpoints. For example, if the endpoints of the line segment are (x1, y1) and (x2, y2), the midpoint can be found by using the midpoint formula:

Midpoint = [(x1 + x2) / 2, (y1 + y2) / 2]

2. Find the slope of the given line segment using the slope formula:

Slope = (y2 – y1) / (x2 – x1)

3. The perpendicular bisector will have a slope that is the negative reciprocal of the slope of the original line segment. To find the negative reciprocal, take the inverse of the slope and change the sign. For example, if the slope of the original line segment is m, the slope of the perpendicular bisector will be -1/m.

4. Use the midpoint found in step 1 and the slope found in step 3 to write the equation of the perpendicular bisector in the slope-intercept form (y = mx + b) or the point-slope form ((y – y1) = m(x – x1)).

5. Finally, simplify the equation to find the perpendicular bisector.

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