Question

Prove using coordinate geometry: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Answer 1

choose the perpendicular bisector to be the \(y\)-axis, and the length of the segment \(2a\), so that \(Q(-a,0)\) and \(R(a,0)\)

compute \(\overline{PQ}\) and \(\overline{PR}\)

Answer 2

let \(P(0,y)\)