Perpendicular bisector of a segment as an InfiniteLine
PerpendicularBisector[{p1, p2}]
PerpendicularBisector[Line[{p1, p2}]]
bisector = PerpendicularBisector[{{0, 0}, {0, 1}}]
→ InfiniteLine[{0, 1/2}, {1, 0}]bisector = PerpendicularBisector[Line[{{-1, -1}, {1, 1}}]]
→ InfiniteLine[{0, 0}, {2, -2}]bisector = PerpendicularBisector[{{a, b}, {c, d}}]
→ InfiniteLine[{(a + c)/2, (b + d)/2}, {-b + d, a - c}]