Perpendicular Bisector Calculator
Midpoint, slope and equation of the bisector.
Enter your values
Enter the x₁ you are working with.
Enter the y₁ you are working with.
Enter the x₂ you are working with.
Enter the y₂ you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Bisector equation
- y = -2x + 9
- Midpoint
- (2, 5)
- Segment slope
- 0.5
- Bisector slope
- -2
- Segment length
- 8.9443
Quick answer
The perpendicular bisector passes through the midpoint of a segment with slope equal to the negative reciprocal of the segment's slope.
y − y_m = −1/m (x − x_m)
At a glance
| What it does | Midpoint, slope and equation of the bisector. |
|---|---|
| Category | Math |
| Inputs needed | x₁, y₁, x₂, y₂ |
| Main output | Bisector equation |
| Formula | y − y_m = −1/m (x − x_m) |
| Cost | Free — no sign-up, no download |
How to use the Perpendicular Bisector Calculator
- 1Enter the coordinates of the first point.
- 2Enter the coordinates of the second point.
- 3Read the midpoint and bisector equation.
Inputs explained
- x₁
- Enter the x₁ you are working with.
- y₁
- Enter the y₁ you are working with.
- x₂
- Enter the x₂ you are working with.
- y₂
- Enter the y₂ you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- x₁-2
- y₁3
- x₂6
- y₂7
Results
- Bisector equationy = -2x + 9
- Midpoint(2, 5)
- Segment slope0.5
- Bisector slope-2
- Segment length8.9443
Frequently asked questions
What slope does a perpendicular bisector have?
The negative reciprocal of the segment's slope — if the segment has slope 2, the bisector has slope −½.
What if the segment is horizontal?
The bisector is vertical, so it is written as x = midpoint rather than in y = mx + b form.
What do I need to enter into the Perpendicular Bisector Calculator?
Just 4 values: x₁, y₁, x₂, y₂. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Perpendicular Bisector Calculator work out the answer?
The perpendicular bisector passes through the midpoint of a segment with slope equal to the negative reciprocal of the segment's slope. It applies the formula y − y_m = −1/m (x − x_m) and shows the working so you can check each step by hand.
Is the Perpendicular Bisector Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.