# How do we construct the perpendicular bisector of a segment to find its midpoint?

Please see below.

The following way constructs the perpendicular bisector and also finds the midpoint of the given line segment.

Let us consider the line segment

Now open a compass so that distance between tip of the needle and pencil tip is more than half the segment

Now with center at

Do not change radius i.e. distance between tip of the needle and pencil tip and now draw two more arcs, now with

The figure appears as shown below.

Now if we join the two intersection points of arcs, we get the perpendicular bisector of line

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To construct the perpendicular bisector of a segment to find its midpoint, follow these steps:

- Draw the given segment using a ruler.
- With a compass, place the compass tip at one end of the segment and draw an arc that intersects the segment.
- Without changing the compass width, place the compass tip at the other end of the segment and draw another arc that intersects the segment.
- Draw a straight line connecting the points where the arcs intersect the segment. This line is the perpendicular bisector of the segment.
- Use a ruler to extend the perpendicular bisector line beyond the segment.
- Where the perpendicular bisector intersects the segment is the midpoint of the segment.

This process ensures that the line drawn is both perpendicular to the segment and passes through its midpoint, thus effectively bisecting the segment into two equal parts.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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