Vertical bisector of a line or circle is important to find in many areas, including the mechanical field, architecture, or even in space studies. To find the vertical bisector of a line and circle accurately, there are two methods, including manual and by calculators.
In this article, we will discuss both options, including some of the best online calculators to find them.
Before you continue to find the methods of calculation, you should know what the vertical bisector is and what the vertical bisector is.
What is perpendicular bisector and what are its uses?
Talking about the general meaning of the perpendicular it means to bisect something into two equal parts like bisecting a line or a circle. Remember, the perpendicular bisector always happens at the angle of 90 to make the parts equal.
In the above figure, the line between the PQ is cut into two equal parts while it’s bisected by the line AB. This bisection happens at the angle of 90 which makes two equal parts. If the bisecting line doesn’t cross the PQ at the angle of 90 then this will be known as the bisector of PQ.
In the above graph, point F is known as the midpoint of the line PQ while it may become the midpoint of the line AB if the drawn line is equal to PQ.
The bisector can also cross the line segments while it can also be a line segment that ends at the midpoint at shown in the graph below:
Uses of Perpendicular bisector
The architect uses the perpendicular bisector phenomena to draw maps according to the standard. For example, if the architect wants to divide the garden into two equal parts then bisector of the line term can be used.
However, there are more things in architecture where the bisector is used like placing the space for trees, interior designing, lighting, and other information.
This is also used in engineering that is related to aerospace. For example, if you are an engineer at NASA and your project is to make the make a Fuselage for a spaceship. Now, it looks circle when you see from one angle while it looks perimeter of a circle from another angle from where we can see the material used to make. Now, when dividing the circle through bisector will be easy for making your spaceships interior.
How to calculate the perpendicular bisector manually?
Calculation through manual calculation:
One of the ways of finding the perpendicular bisector is manual and here is the way:
- Measure the midpoint of the line: This is the first step where you have to mention the two points along a line and these points with x and y, respectively. Now use the following formula:
[(x1 + x2)/2, (y1 + y2)/2]
This way, you get the average of the points x and y coordinates which will tell you the midpoint of the line.
- Getting slope of the two points: After you get the midpoint, you need to find the slope of the two points and the following formula will be used to get the slope of the two points:
(y2 – y1) / (x2 – x1)
The slope of the line means to find the distance of the line that is vertical after the distance of the horizontal line gets changed.
- Go for getting the negative reciprocal of this slop: After getting the slope of the two points, you need to find the negative reciprocal of this slope for two points. It’s easy as you just need to find the reciprocal and change the sign of the slope. Through flipping the x and y coordinates and changing the sign, you get the reciprocal of the slope.
For example, if the slope of the two points is ½ then the negative reciprocal would be -2.
- Find the equation of the line: The general equation of the line is: y=mx + b, and by putting the value of slope in the position of m and putting the value of x and y, you will obtain the value of b. Once you get the value of b, put the value of slope and b to get the equation of the line. This equation of the line is the perpendicular bisector of the two points.
Calculation through online calculators:
Another way of finding the perpendicular bisector of a line or a circle is through online calculators. Numerous online calculators are available for free that would help you to find the bisector. Below are some of the online calculator that is leading the market for finding this solution:
Meracalculator is an online and free tool for finding math and other educational equations. The perpendicular bisector equation calculator by Meracalculator is the best because it automatically finds with just a few data. You need to enter the details about the value of x1, x2, y1, y2.
Once you enter the value, it would automatically find the perpendicular bisector equation of the line.
For example, I entered the value of (3,4) as (x1, x2) and (4,5) as (y1, y2) and instantly, I got the result as shown below:
This is another tool for those who are finding the perpendicular bisector equation of a horizontal line. This too requires some basic information for two points including x1, x2, y1, y2. This is a free tool without any registration or any type of subscription.
In this calculator, we entered the same value as in the above calculator which is (3,4) as (x1, x2) and (4,5) as (y1, y2). And we got the answer as shown below:
In today’s world, the students as well as the professionals have less time to perform their tasks. So, using the online calculators, we can solve these equations within seconds and without any errors. Manually doing so might involve the human or solving errors but do through the online calculators is much better.