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 = (X_A + X_B)/2

x₁ = (4+16)/2

x₁ =10

y₁ = (Y_A + Y_B)/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