Perpendicular Bisector Calculator

How to use a perpendicular bisector calculator?

  1. Enter the values of the x & y coordinates.
  2. Click calculate button.
  3. Hit the reset button to enter a new function.

Result

Step by step solution:

Data:



Formula:

Solution:

Perpendicular Bisector Calculator

The perpendicular bisector calculator generates an equation of the line which bisects the line at 900.


What is a perpendicular bisector?


Perpendicular means it will make an angle of 900 and the bisector means it will cut it into two equal parts. So the perpendicular bisector is a line that makes an angle of 900 and divides into two equal parts.


 Perpendicular Bisector formula:

 

The equation of perpendicular bisector is:

y - y1 = m (x – x1)

Where x1 & y1 are the midpoints points of the given coordinate points and "m" is the slope of the line calculated by using the x & y coordinate points of the line.

 

How to calculate a perpendicular bisector?


To calculate the perpendicular line bisector equation the following calculation must be taken for getting the result. 

  • Find the midpoint from the given vertices.
  • Calculate the slope of the perpendicular line.
  • Put all the values in the formula of the perpendicular bisector line.

Example:

Find the perpendicular bisector of the line having vertices (4, 16) and (12, 32).

Solution:

Step 1: We have to find the mid-point from the given vertices.

x1 = (XA + XB)/2

x1 = (4+16)/2

x1 =10


y1 = (YA + YB)/2

y1 = (12+32)/2

y1 = 22

So, the mid-point is (10,22).

Step 2: Now calculate the slope of the line.

m = (32 - 12)/ (16-4)

m = 1.67

Step 3: Now take the negative reciprocal of the slope to get the slope of the perpendicular line.

The slope of the perpendicular line is:

m = -1/m

m = -1/1.67

m = - 0.6 

Step 4: Substitute the value in the general expression of the perpendicular bisector.

y - y1 = m (x – x1)

y – 22 = -0.6x + 6

y = -0.6x +28

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