How to find the midpoint of a line segment?

In this guide, two simple procedures will be explained How to find the midpoint of a line segment? The point of a segment in geometry is one of the most important arguments in order to be able to solve many exercises. A segment, in geometry, is a “portion” of a straight line that, unlike the latter, has a beginning and an end, and is identified by 2 fixed points, called for this reason “extremes”, which in turn are congruent or also called isomerically.

How to find the midpoint of a line segment?

Main formula to find the midpoint of a line segment is m = (xA + xB)/2, (yA + yB)/2

First Method.

This is the first method for finding the midpoint of a segment. Considering our segment “AB”, we proceed with tracing it on the sheet using a ruler, and remembering to identify the extremes, naming them with the letters “A” and “B”.

From a mathematical point of view, half of the segment corresponds to the ratio of the length between a and b divided by two.

In order to proceed from a practical point of view, you can move on to the next step which is explained in the next step of the guide.

Find the point AB

To proceed From a practical point of view it is necessary to have two squares and a compass.
Take the latter and put the tip on “A” with the opening “AB”.

Draw an arc both above and below the segment.
Then repeat the process, this time pointing the compass at “B”, always keeping the opening “AB”. We are almost there. The next step is missing.

Locate the CD point

At this step you will have identified two points, which we will call “C” and “D”. They are formed by the intersection of the two arcs of the circumference that you have drawn earlier.

Now you have to proceed by taking a ruler, and you have to join these two points together.
The point where the “CD” segment meets the “AB” segment perpendicularly is the exact midpoint, which you can identify with the letter “M”. That’s it to be able to find the midpoint of a segment. At this point you can also go ahead with the guide to be able to see the second method.

Perform the second method

In addition to the method just explained, there is another one. This second way of finding the point of a segment is even simpler than the one explained above. To be able to implement it, you simply need to use two brackets and a pencil.

We start by drawing the “AB” segment. We take a bracket and stop it exactly above and parallel to the segment.
At this point, with the other square, we slide the surface of the square held firm, and, having positioned the second square with the beginning on point “B”, we draw a line perpendicular to the segment of length “AB”.

Connect the points AB and CD

Continue by repeating exactly the same procedure on “A”.
We name the end points of the segments drawn by “A” and “B” as “C” and “D” respectively.
Then we join points “A” and “D” and “B” and “C” with two other segments.
At this point, we will call “M” the intersection of the two segments “AD” and “BC”.

Find point M

At this point we are almost at the end, the last step consists in taking a bracket and placing it parallel to the “AB” segment.

Then, with the other, slide the parallel square until the second one passes perfectly through the “M” point. It is now possible to trace a segment from “M” to “AB”.

The point where the next traced segment touches “AB” is its midpoint.
Let’s name it with “P”. Finding the midpoint of a segment is not difficult. It is a simple but essential exercise in geometry.

Suzanna N. Alejos

I am Suzanna Alejos. I write articles for many different online publications, and manage my own blog where I share my thoughts on a variety of topics.

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