# The perpendicular bisector of a line segment:

Fold a sheet of paper. Let bar"AB" be the fold. Place an ink-dot X, as shown, anywhere.

Find the image X' of X, with AB as the mirror line.

Let bar"AB" and bar"XX’" intersect at O.

This means that bar"AB"  "divides"  bar"XX’" into two parts of equal length.

bar"AB"  "bisects"  bar"XX’" or bar"AB"  "is a bisector of"  bar"XX’".

Hence, bar"AB"  "is the perpendicular bisector of"  bar"XX’".

## Construction using ruler and compasses:

Step 1: Draw a line segment bar"AB" of any length.

Step 2: With A as the centre, using compasses, draw a circle. The radius of your circle should be more than half the length of bar"AB".

Step 3: With the same radius and with B as centre, draw another circle using compasses. Let it cut the previous circle at C and D.

Step 4: Join bar"CD". "It cuts"  bar"AB" at O.

Use your divider to verify that O is the midpoint of bar"AB".

Therefore, bar"CD"  "is the perpendicular bisector of"   bar"AB".

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Perpendicular Bisector of the Line Segment [00:01:24]
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