Find the equation of the perpendicular bisector

 Find the equation of the perpendicular bisector

To find the equation of the perpendicular bisector of a given line, you need to follow these steps:

1. Determine the slope of the given line. Let's denote it as m

2. Find the negative reciprocal of the slope. The negative reciprocal is obtained by flipping the fraction and changing the sign. Let's denote the negative reciprocal as -1/m.

3. Determine the midpoint of the line segment defined by the given line. To find the midpoint, average the x-coordinates and the y-coordinates of any two points on the given line. Let's denote the midpoint as (x₀, y₀).

4. Use the negative reciprocal slope and the midpoint to write the equation of the perpendicular bisector in point-slope form. The point-slope form of a line is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line.

   The equation of the perpendicular bisector is:

   y - y₀ = (-1/m)(x - x₀)

   Simplify if necessary.

5. Convert the equation to a desired form, such as slope-intercept form (y = mx + b) or standard form (Ax + By = C), depending on the requirements of the problem.

That's how you find the equation of the perpendicular bisector of a given line