- Enter the values of the x & y coordinates.
- Click
**calculate**button. - Hit the
**reset**button to enter a new function.

Result

**Data:**

**Formula:**

**Solution:**

The perpendicular bisector calculator generates an equation of the line which bisects the line at 90^{0}.

What is a perpendicular bisector?

Perpendicular means it will make an angle of 90^{0} and the bisector means it will cut it into two equal parts. So the perpendicular bisector is a line that makes an angle of 90^{0} and divides into two equal parts.

Perpendicular Bisector formula:

The equation of perpendicular bisector is:

**y - y _{1} = m (x – x_{1})**

Where x_{1} & y_{1} 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.

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.

x_{1} = (X_{A} + X_{B})/2

x_{1} = (4+16)/2

x_{1} =10

y_{1} = (Y_{A} + Y_{B})/2

y_{1} = (12+32)/2

y_{1} = 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 - y_{1} = m (x – x_{1})

y – 22 = -0.6x + 6

y = -0.6x +28

6 months ago

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