Using ruler and compasses construct:
the locus of points equidistant from $$A$$ and $$B$$.
Steps of construction:-
(i) Draw a line segment $$AB$$
(ii) Taking $$A$$ as centre and radius greater than $$\dfrac12 AB, $$ construct arc above and below the line segment $$AB$$
(iii) Taking $$B$$ as centre and radius greater than $$\dfrac12 AB, $$ construct arc above and below the line segment $$AB$$ to cut the previous arc at $$C\,\&\,D$$
(iv) join $$CD$$
(v) $$CD$$ is perpendicular bisector of line segment $$AB$$
(vi) $$CD$$ is the locus of points equidistant from points $$A$$ and $$B$$