A line segment is symmetrical about its:
perpendicular bisector
Line of Symmetry is an imaginary line or axis that divides a shape or figure into two exactly similar or identical halves and line of symmetry generally passes through the centre of the shape.
We know that only the straight line which passes through the centre of the line segment at right angle divides the line segment in the two similar or identical halves, which means that the line of symmetry of a line segment is the perpendicular bisector of the line segment.
Therefore, the line of symmetry of a line segment is the perpendicular bisector of the line segment.
Hence option A is correct.