What is a Perpendicular Bisector?

A perpendicular bisector is a line that passes through the midpoint of a given line segment and is perpendicular (forms a 90-degree angle) to that line segment. It divides the original line segment into two equal parts and is always at right angles to it. Perpendicular bisectors have important applications in geometry, including finding the center of a circle or locating points equidistant from two given points.

How to Use the Perpendicular Bisector Calculator

Step 1: Enter the coordinates of the first point

Input the x-coordinate and y-coordinate of the first point of your line segment into the respective fields labeled "Point 1 X-coordinate" and "Point 1 Y-coordinate". These values can be positive, negative, or decimal numbers.

Step 2: Enter the coordinates of the second point

Input the x-coordinate and y-coordinate of the second point of your line segment into the fields labeled "Point 2 X-coordinate" and "Point 2 Y-coordinate". Again, these can be any real numbers.

Step 3: Click the "Calculate Perpendicular Bisector" button

After entering all four coordinates, click the blue "Calculate Perpendicular Bisector" button. The calculator will process your input and generate the results.

Step 4: Interpret the results

The calculator will display three pieces of information:

• The equation of the perpendicular bisector in the form y = mx + b, where m is the slope and b is the y-intercept.
• The coordinates of the midpoint of your original line segment.
• An explanation of what the equation represents in relation to your input points.

Step 5: Use the results for further calculations or geometric constructions

You can use the equation of the perpendicular bisector for various geometric problems, such as finding points equidistant from your original points or determining the center of a circle that passes through both points.

By following these steps, you can easily find the equation of a perpendicular bisector for any two points in a coordinate plane. This tool is particularly useful for students studying geometry, engineers working on spatial problems, or anyone needing to find a line that's perpendicular to and bisects another line segment.