What is perpendicular bisector?
How does an archaeologist assess the size of a surface if there is only one piece of it? How does a landscaper assess the placement of sprinklers for the most efficient use of water? It points out that in each of these concerns a single line, named the perpendicular bisector, can be very important.
The line segment AB perpendicular bisector is a line which includes two main aspects:
- Split the line segment AB into or bisects equal size sections
- Allows a right angle with the AB (perpendicular) line segment
The perpendicular bisector at point C intersects section AB. The distance from point A to point C is similar to that between point B and point C. A valuable aspect is that each position on the perpendicular bisector is the same distance between point A and point B.
Online perpendicular bisector calculator
Students find it very hectic to calculate or finding geometrical theorems manually when they have variety of options available online. Now, in the age of technology and science there is a solution to every problem. Multiple online calculators help you determining the perpendicular bisector step by step.
Meracalculator provides Perpendicular Bisector Calculator that is a digital geometric computation tool designed to figure out a line’s perpendicular bisector by the coordinates given (x1, y1) and (x2, y2). A perpendicular bisector in geometry is a set of points that are equidistant from coordinates that are (x1, y1), and (x2, y2).
Each point on the perpendicular bisector is as far as coordinates (x1, y1) and coordinates (x2, y2) are concerned. In this calculator, the given line coordinates (x1, y1) and (x2, y2) in the XY plane are used to figure out a line’s perpendicular bisector.
Finding the perpendicular bisector manually
To identify the two-point perpendicular bisector, all you have to do is determine their midpoint and reciprocal negative and put those results into the slope-intercept line equation. Below is the step by step guidance to find the perpendicular bisector of two points easily.
Formula to find the perpendicular bisector
The general formula for perpendicular bisector is
y – y1 = m (x – x1)
- Here m is representing the slope that equals to (y2-y1)/(x2-x1)
- Y2 and y1 are the two y coordinates
- x2 and x1 are the two x coordinates
Follow the given steps for finding the perpendicular bisector of two points
Finding the midpoint
The first step of determining the perpendicular bisector is simply finding out the midpoint of these two lines or points. To determine the midpoint, simply inserted them into the midpoint formula that is represented as
(x1 + x2)/2
(y1 + y2)/2
For finding out the midpoint of the two coordinates, it is significant step to take the sum of the two sets of points’ x and y coordinates. Let’s assume you are dealing with the coordinates
(x1, y1) = (6, 4)
(x2, y2) = (10, 4)
Here’s the midpoint for those two points.
- = [(6+10)/2, (4 +4)/2]
- = (16/2, 8/2)
- = (8, 4)
So, the midpoints are 8 and 4
Next step is finding out the slops of two points and it is also a simple step, you need to put the slop formula of two points and that’s it. The slope of the two points can be determined simply by the slope formula that is represented as
(y2 – y1) / (x2 – x1)
If we simply define a slop, then a slop measures the distance of its vertical change over the distance of its horizontal change. Here is the justification to find the slope of the line that goes through the points
(x1, y1) = (6, 4)
(x2, y2) = (10, 4)
Slop = (y2-y1)/(x2-x1)
= (4-6)/ (10-4)
As a result, the slope of the line we get is -1/3. But for determining this slope, you need to cut 2/6 to its lowest terms as1/3, it is because the both numbers are evenly divisible by 2.
Negative reciprocal of the slop of two points
It is easy to take the reciprocal negative of a slope; all you need to do is taking the slope’s reciprocal and change the sign. You can take the reciprocal negative of a number by easily switching the coordinates x and y and changing the symbol. 1/2 is -2/1, or only -2; the opposite of -4 is 1/4.
3 is the reciprocal negative of -1/3, it is because 3/1 will be the reciprocal of 1/3 and it is obvious that the sign has shifted from negative to positive.
Now you have found the slope as above so you can solve the equation with the value of slope and the midpoints.
Let’s say find the equation of the AB with
Y = mx + b
Here slop is equaled to m = 3
Thus, the equation becomes
Y = 3x + b
Now the midpoints are x, y = 8, 4
The next step is taking the values of x and y and put them in the equation
4= 3 x 8 + b
4= 24 +b
b= 4 -24
b = -20
m = 3 and b = -20
so, the final equation of perpendicular bisector between two points becomes
y = mx + b
y = 3x -11
Thus, the perpendicular bisector of two points x and y equal to y = 3x -11.
By Ezza Dugan
who writes for business marketers and SEO tool users to make their websites rank on google. She has written for a number of websites i.e., calculators(.)tech, inside tech box and eLearning industry. She is a regular contributor to prepostseo(.)com with most digital marketing, SEO techniques, and tech-related articles.