Constructing a Perpendicular Bisector | Steps, Properties, and Applications in Math and Geometry

Perpendicular Bisector

A perpendicular bisector is a line or a line segment that is perpendicular to a given line segment and divides it into two equal parts

A perpendicular bisector is a line or a line segment that is perpendicular to a given line segment and divides it into two equal parts. In other words, it is a straight line that cuts another line segment into two equal halves at a 90-degree angle.

To construct a perpendicular bisector, follow these steps:
1. Take the line segment and draw arcs of the same radius from both endpoints.
2. With the compass set to a radius greater than half the length of the line segment, draw two arcs on either side of the line segment.
3. Connect the intersections of the arcs on each side of the line segment using a straight edge, forming a straight line that cuts the line segment perpendicularly. This line is the perpendicular bisector.

The key properties of a perpendicular bisector are:
1. It divides the line segment into two equal halves.
2. It is perpendicular to the line segment it bisects.
3. It is equidistant from the endpoints of the line segment. This means that the distance from any point on the perpendicular bisector to each endpoint of the line segment is the same.

Perpendicular bisectors have various applications, particularly in geometry and construction. They are used to find the midpoint of a line segment, construct right angles, and determine equidistant points from a given point. They also play a significant role in trigonometry and coordinate geometry, as they help determine the equation of a line when the coordinates of its endpoints are known.

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