Geometry, Data and Neighbors Predict People’s Favorite Movies

Because it lies on the perpendicular bisector of segment $latex \overline{AB} $, point Q is equidistant to A and B. Since every point on the perpendicular bisector of segment $latex \overline{AB} $ is equidistant to A and B, we have another powerful way to think about the perpendicular bisector: as a dividing line. Similarly, everything on Adrienne’s side of $latex \overline{AB} $’s perpendicular bisector is closer to Adrienne than to Brandon.

Source: www.quantamagazine.org