What you’ll learn
Construct perpendicular bisectors.
Key idea
The opening must allow two crossings on opposite sides; equal radii give equal endpoint distances.
Two crossings from identical endpoint openings locate the bisector; a line through unequal-radius crossings need not bisect.
Worked example
Enter the exact value or ordered values in the format requested below.
Segment A=(-2, 1), B=(8, 1), length AB=10; call equal-opening arc crossings P,Q. Construct its perpendicular bisector using radius AB. Enter centers=...; arcs=...; radius=...; line=... .
- Using radius AB=10, both circles cross twice; midpoint horizontal coordinate 3, vertical offset squared 75.
- Both crossings have equal distances to A/B; line PQ is perpendicular to AB and passes its midpoint.
Answer: centers=A,B; arcs=both_sides; radius=AB; line=PQ
Quick Check
Choose which candidate representation satisfies the requirements of 'Construct perpendicular bisectors' and justify the choice.
Segment A=(0, -2), B=(4, -2), length AB=4; call equal-opening arc crossings P,Q. Candidate 1: same opening AB at A/B, arcs both sides, join P/Q. Candidate 2: arc from A only, draw AP. Candidate 3: unequal openings at A/B, join two crossings. Select with equidistance evidence.