A perpendicular bisector is a line that is perpendicular to a line segment and divides the line segment exactly into two halves by passing through the midpoint of the line. ‘Bisect’ is the term that indicates the division into two equal parts. Perpendicular means a line making an angle of 90 degrees with another line. Perpendicular bisector makes 90-degree angles with the line segment on both sides of the line. The midpoint is the point on the line which is equidistant from the two endpoints of the line segment. So it can be said that any point on the perpendicular bisector is also at equal distances from the endpoints of the line segment. There can be only one perpendicular bisector because a line segment has only one midpoint.
Important Points About Perpendicular Bisector
- It divides a line segment into two halves.
- It makes an angle of 90 degrees at the point of intersection with the line.
- It passes through the midpoint of the given line segment.
- The distance of any point on the perpendicular bisector is equal to both the endpoints of the line.
Drawing a Perpendicular Bisector
The steps to draw a perpendicular bisector of a line segment are as follows:
- Draw a line segment AB of any suitable length.
- Taking A as the center and radius of more than half of the line segment AB, draw arcs with the help of compass above and below the line segment.
- Repeat the above step taking B as the center so that the second arcs intersect the previous arcs.
- Indicate the points of intersection above and below the line as ‘M’ and ‘N’ respectively.
- Join the points ‘M’ and ‘N’. The point at which the line MN intersects the line segment AB is marked as ‘O’
- The line MN is the perpendicular bisector of line AB and passes through the midpoint O of AB.
What are Perpendicular Lines?
A line is said to be perpendicular to another straight line when the angle formed between them is 90 degrees or right angle. So any line intersecting another line at a right angle is said to be perpendicular to that line. Both the straight lines are perpendicular lines as they are perpendicular to each other when they form a right angle at the point of intersection. A perpendicular bisector is also a perpendicular line that intersects a line segment at the midpoint. Learn this topic in detail from Cuemath.
Two straight lines can intersect each other at any angle but they are not always perpendicular to each other. The intersecting lines can be said to be perpendicular only when they satisfy the following conditions. The properties applicable to perpendicular lines are as follows:
- Perpendicular lines always form at a right angle at the point of intersection.
- A given line can have multiple intersecting perpendiculars that will be parallel to each other.
Drawing a Perpendicular Line
Drawing a perpendicular line to a given line segment can be done by the following simple steps.
- A horizontal line XY of a certain length is to be drawn.
- The midpoint M of the line XY is marked.
- Taking midpoint M as the center, two arcs are drawn with help of a compass so that the arcs intersect the line at two points A and B which are equidistant from the midpoint M.
- Again by taking A and B as centers respectively, two arcs are drawn inside such that the arcs intersect each other at the top and below of the horizontal line.
- The two points where the arcs intersect are marked as P and Q.
- By joining P and Q we get a line that intersects the horizontal line at 90 degrees.
- The line PQ is perpendicular to the line segment XY.