Perpendicular Bisectors from a Point
This activity belongs to the GeoGebra book GeoGebra Principia.
The Field of Equidistant Perpendicular Bisectors from a Fixed Point and another Free Point on a Fixed Line
Let r be the line passing through the fixed points O and I. Let A be a point on r. We will call mA the perpendicular bisector of the segment OA.
Now, it's sufficient to extend all the operations already seen between two points A and B to the corresponding ones between perpendicular bisectors mA and mB.
If we align the coordinate origin with O and point (1, 0) with I, the point P corresponds to (p, 0), allowing us to represent the perpendicular bisector mP with the equation: x = p/2.
Author of the construction of GeoGebra: Rafael Losada.