How it works

This calculator helps you find the equation of the perpendicular bisector of a line segment defined by two points. A perpendicular bisector is a line that cuts a segment exactly in half at a 90-degree angle.

The Formula

To find the perpendicular bisector, we first calculate the midpoint of the segment using M = ((x1+x2)/2, (y1+y2)/2). Then, we find the slope of the segment, m = (y2-y1)/(x2-x1). The perpendicular slope is -1/m. Finally, we use the point-slope form (y - y_m = m_perp * (x - x_m)) to get the equation of the bisector.

Worked Example

1. Example: Points (1, 2) and (5, 6)

   Let's find the perpendicular bisector for points A(1, 2) and B(5, 6). 1. Midpoint: ((1+5)/2, (2+6)/2) = (3, 4). 2. Slope of AB: (6-2)/(5-1) = 4/4 = 1. 3. Perpendicular slope: -1/1 = -1. 4. Using point-slope form with midpoint (3, 4) and slope -1: y - 4 = -1(x - 3) => y - 4 = -x + 3 => y = -x + 7. So, the perpendicular bisector is y = -x + 7.

Tips, Assumptions & Limitations

• Ensure your coordinates are entered correctly for both points.
• Remember that a vertical segment will have a horizontal bisector (y = constant), and a horizontal segment will have a vertical bisector (x = constant).
• The perpendicular bisector is equidistant from the two original points.