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# Perpendicular Bisector Calculator

Enter Values in the given input box to find Perpendicular bisector equation using our Perpendicular bisector calculator.

**Perpendicular bisector equation Formula**

`y-y1 = m(x-x1)`

The bisector can either cross the line segment it bisects, or can be a line segment or ray that ends at the line.

Perpendicular line equation calculator used to find the equation of perpendicular bisector. It is also known as angle bisector.

*What is perpendicular?* *What is a perpendicular bisector?* *How to find a perpendicular line?*** **These are the questions we are going to answer in this space.

## Perpendicular bisector definition

Perpendicular Bisector is the division of something into two equal or congruent parts. It is a line, ray, or segment which cuts another line segment into two equal parts at 90 degrees.

The perpendicular bisector equation can be effortlessly calculated using the perpendicular bisector calculator. Constructing a perpendicular bisector could be convenient if you know how to use a compass?

### Perpendicular Bisector of a line segment

If a line is perpendicular to another line and dividing into two equal parts, it will be a perpendicular bisector of a line segment. See the figure below:

Use the perpendicular line calculator** **to calculate the perpendicular bisector equation.

### Perpendicular Bisector of a Triangle

If a line is perpendicular to the side of a triangle and crossing it through the midpoint, it will be the perpendicular bisector of a triangle.

### Perpendicular Bisector of a Circle

If a line is perpendicular to a chord of a circle and passes through the midpoint of that circle, it will be the perpendicular bisector of a circle.

### Perpendicular Bisector of a Rhombus

The diagonals of a rhombus are the perpendicular bisector of the rhombus as those diagonals are always perpendicular to each other dividing the sides of the rhombus into two equal parts.

## How to find perpendicular bisector?

**Example:**

Let's find the perpendicular bisector equation with points P(3,4) and Q(6,6).

**Solution**

Consider the coordinates of the points P and Q to be x1,y1, and x2,y2 respectively. We need to calculate the midpoints of the line PQ, which is F, and the slope to find the equation of the perpendicular bisector.

__Step 1__:

Let's calculate the midpoint of the line which is the average of the x and y coordinates.

Midpoint of a line = x1+x2/2, y1+y2/2

Midpoint of PQ = 3+6/2, 4+6/2 = (9/2, 10/2)

__Step 2__:

Next, we need to find the slope of the line PQ using the formula y2-y1/x2-x1. Kindly note that the slope is represented by the letter 'm'.

Slope of PQ (m) = 6-7/6-5 = -1 = 6-4 /6-3 = 2/3 = 0.4

__Step 3__:

Now, let's calculate the slope of the perpendicular bisector (AB) of the line PQ. The slope of the perpendicular bisector = -1/slope of the line.

Therefore for AB = -1/0.4 = -2.5

__Step 4__:

Once we find the slope as above, we can find the equation with the slope and the midpoints.

Lets find the equation of the AB with midpoints (9/2,10/2) and the slope -2.5.

Formula to find the equation: y-y1 = m(x-x1) y-10/2 = -2.5(x-9/2)

By solving the above, we get the equation** y-5 = -2.5 (x-9/2)**.

This is the perpendicular bisector equation (AB) of the line PQ.compound interest allows your money to earn even more money over time.

**References: **

- Stapel, E. Slope: Parallel & Perpendicular Lines | Purplemath. Purplemath.
- Perpendicular Bisector by study.com
- Perpendicular Bisector Theorem (Proof, Converse, Examples, & Video). Tutors.com.