Draw a line segment of length 9.2 cm and construct its perpendicular bisector using a compass and ruler.

Steps of construction :

(i) Draw a line segment AB = 9.2 cm.

(ii) With A as centre and radius more than half of AB (more than 4.6 cm), draw two arcs, one above and one below AB.

(iii) With B as centre and the same radius, draw two arcs cutting the previous arcs at P and Q.

(iv) Join PQ. The line PQ is the required perpendicular bisector of AB, cutting AB at its mid-point M so that AM = MB = 4.6 cm.

Hence, PQ is the required perpendicular bisector of the line segment AB.