About Perpendicular Bisector Calculator (Formula)
The Perpendicular Bisector Calculator is a geometric tool used to find the equation of the perpendicular bisector of a line segment. The formula for calculating the perpendicular bisector involves several components:
- Midpoint Formula:
- Midpoint (M) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2) Where (x₁, y₁) and (x₂, y₂) are the coordinates of the endpoints of the line segment.
- Slope of the Original Line Segment:
- Slope (m) = (y₂ – y₁) / (x₂ – x₁)
- Slope of the Perpendicular Bisector:
- Perpendicular Slope (m⊥) = -1 / m The perpendicular bisector’s slope is the negative reciprocal of the original line segment’s slope.
- Equation of the Perpendicular Bisector:
- Perpendicular Bisector Equation (y – y₁) = m⊥(x – x₁)
The resulting equation represents the line that passes through the midpoint of the original line segment and is perpendicular to it. This perpendicular bisector divides the original line segment into two equal halves.
The Perpendicular Bisector Calculator simplifies the process of finding this important geometric construct, commonly used in mathematics and engineering for various applications, including navigation, architecture, and design.