Equation Of A Perpendicular Bisector

Enter the coordinates of X and Y to construct the perpendicular bisector line equation using perpendicular bisector calculator.

The perpendicular bisector line equation estimator is an online tool that generates an equation for the perpendicular line bisector past using the points on which that line lies. It shows you lot all steps it used to detect the bisector equation.

What is perpendicular bisector?

Perpendicular bisector can be defined equally,

"A line which divides a line segment into ii equal parts at ninety° making a right angle."

Perpendicular bisector equation

Equation of a perpendicular line bisector is given below.

y – y_one = grand ( 10 – ten₁)

Where,

m is slope of the line, and

x₁ , y_ane are midpoint of the co-ordinates.

How to notice equation of perpendicular bisector?

Example:

Notice the perpendicular bisector equation of line with the points (6, 7), (4, 3).

Solution:

Step 1: identify the values.

10_ane = six, ten₂ = 4

y₁ = 7, y₂ = 3

Step 2: Find the midpoint using the given points.

Midpoint = (x₁ + x₂)/2, ( y₁ + y₂ )/2
= (half-dozen+4)/2, (vii +3)/2
= (ten/ii, ten/two)
= (5, 5)
Midpoint coordinates (x_one , y₂) = (5, v)
Step 3: Find the gradient of line:

Gradient m = (y₂ - y_ane)/(x_ii - x₁)
(3-7)/(4-6)
= ii
Stride iv: Take the negative reciprocal of slope.
m = - (one/2) = - 0.v
Step 5: Place the values in perpendicular bisector equation.
y – y_one = m(x – x₁)
y – v = -0.5(x – 5)
y = -0.5x + seven.v