Perpendicular Bisector Calculator

Enter Values in the given input box to find Perpendicular bisector equation using our Perpendicular bisector calculator(Perpendicular line equation/angle bisector/segment bisector calculator).



Point A:
Point B:
Perpendicular Bisector Equation:

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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. 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 degree.

How to find perpendicular bisector?

Lets find perpendicular bisector equation with points P(3,4), Q(6,6). Consider the co-ordinates 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:
Lets calculate the midpoint of the line which is the average of the x and y co-ordinates.
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, lets 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.mpound interest allows your money to earn even more money over time.


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  2. Perpendicular Bisector (Definition, Properties, and Construction). BYJUS. (2020).
  3. Stapel, E. (2020). Slope: Parallel & Perpendicular Lines | Purplemath. Purplemath.
  4. Perpendicular Bisector (solutions, examples, videos).
  5. Perpendicular Bisector by
  6. Perpendicular Bisector Theorem (Proof, Converse, Examples, & Video).