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The perpendicular bisector passes through the midpoint of a segment at right angles to it, so its gradient is the negative reciprocal of the segment's. Every point on it is equidistant from the two endpoints.
Perpendicular bisector
through ((x₁+x₂)/2, (y₁+y₂)/2) with gradient −(x₂−x₁)/(y₂−y₁)
The midpoint is (4, 4), the segment gradient is 2/3, so the bisector is y = −1.5x + 10.
The perpendicular bisectors of a triangle's sides meet at the circumcentre, the centre of the circle through all three vertices.