Perpendicular Bisector Calculator
Midpoint, slope and equation of the bisector.
Enter your values
Results update instantly as you type — no submit needed.
Results
- 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.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.