Tuesday, April 2, 2013

47-Solution on perpendicular Bisector: Important key points

Today we will see the answer to the question asked in Blog-19.
The question was:

Draw the perpendicular bisector to a line segment drawn at the bottom of the page as shown in the following diagram.

We know the procedure to draw the perpendicular bisector of a line segment.
1) In a compass,  take a distance of more than half the segment.
[ Here my question is why do we need to take the distance more than half? ]
Here the Answer is very simple. You will come to know it very soon while discussing the basic of drawing perpendicular bisector on the line segment.

2) Taking Point A as the center and radius as more than half the distance of the segment, Draw the arcs on both side of the segment.

3) Repeat the same by taking point B as the center and with the same radius.

Now you will get the answer to the question why do we need to take the radius as more than half. The arcs drawn with center A and center B should intersect each other.

4) Then join these two points to draw the line which is perpendicular bisector of the segment AB.
As per the Geometry is concern, we can draw the perpendicular bisector by the same way.
Here we must understand the Basic Concept of a perpendicular bisector. It is already available in the procedure itself. As we are drawing the arcs with the same radius and the centers as point A and point B on both sides of the segment to get two points which are the point of intersection of these arcs. 

As per the question, so many students say their views as follows.

Some students said that the question is wrong as the line segment on which perpendicular bisector is to be drawn is at the bottom of the paper. It must be in the middle of the paper.

Some students said that the perpendicular bisector is not possible as we can't draw the intersecting arcs below the segment. The segment should be a little bit above.

Some students said that some additional blank paper needs to place below the line segment and construct the perpendicular bisector.

I surprised by listening to these answers. The above problem can be solved simply by applying the basics of perpendicular bisector.

We must know that every point of the perpendicular bisector is at an equidistant from the endpoints of the segment. So do the following steps to draw the perpendicular.

1) Take radius more than the half of the line segment AB.
2) Take point A as the center, draw an arc above the segment AB.
3) Take point B as the center, draw an arc above the segment AB.
4) Name the point of intersection of these arcs as point C.
5) Increase the radius and draw two intersecting arcs with centers A and B above the Point C
6) Name this point of intersection of these arcs as point D.
7) Draw line joining points C and D.
Please see the following diagram to understand more about the concept.

Here Points C and D are at equidistant from the endpoints A and B. So line CD is the perpendicular Bisector of line segment AB.

We all together think properly to understand the basic concepts of Math. We will definitely change the entire world to understand better basics of Math along with other subjects.

Anil Satpute

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