Question

What is the no of perpendicular bisector of a line segment?

Answer 1

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perpendicular bisector when the bisector intersects the segment at a right angle.

DE←→ is the perpendicular bisector of AC¯¯¯¯¯¯¯¯, so AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ and AC¯¯¯¯¯¯¯¯⊥DE←→.

For every line segment, there is one perpendicular bisector that passes through the midpoint. There are infinitely many bisectors, but only one perpendicular bisector for any segment.

Answer 2

Answer:

A perpendicular bisector can be defined as a line segment which intersects another line perpendicularly and divides it into two equal parts. Two lines are said to be perpendicular to each other when they intersect in such a way that they form 90 degrees with each other. And, a bisector divides a line into two equal halves. Thus, a perpendicular bisector of a line segment AB implies that it intersects AB at 90 degrees and cuts it into two equal halves.

Properties of a Perpendicular Bisector

• It divides AB into two equal halves or bisects it.

• It makes right angles with (or is perpendicular to) AB.

• Every point in the perpendicular bisector is equidistant from point A and B.

While working with practical geometry, you will often find the application of perpendicular bisectors; say when you are asked to draw an isosceles triangle, or when you have to determine the centre of a circle, etc. Below are the steps to construct a perpendicular bisector of a line using a compass and a ruler.

How to Construct a Perpendicular Bisector?

You will require a ruler and compasses. The steps for the construction of a perpendicular bisector of a line segment are:

• Step 1: Draw a line segment PQ.

• Step 2: Adjust the compass with length a little more than half of the length of PQ.

• Step 3: Place the compass pointer at point P and draw arcs above and below the line.

• Step 4: Keeping the same length in the compass, place the compass pointer at point Q. Similarly, draw two arcs above and below the line keeping the compass pointer at Q.

• Step 5: Mark the points where the opposite arcs cross as X and Y.

• Step 6: Using a ruler, draw a line passing across X and Y.

The perpendicular bisector bisects PQ at a point J, that is, the length PJ is equal to JQ. And the angle between the two lines is 90 degrees.