Let's Recall

Let's Recall

Before we formally define a locus, it helps to recall two shapes you already know well from geometry class, because both are secretly defined by an equidistance condition — exactly the pattern a locus follows.

• Perpendicular bisector of a segment. Given a segment $AB$, the perpendicular bisector is the set of all points $P$ in the plane with $PA = PB$. Every such point is equidistant from $A$ and $B$, and this whole collection of points turns out to be a straight line.
• Bisector of an angle. Given an angle with arms $OA$ and $OB$, the bisector is the set of all points equidistant from the two arms, i.e. every point $P$ with $\angle POA = \angle POB$. This whole collection of points turns out to be a ray.

Both of these are sets of points satisfying a condition — which is exactly the definition of a locus we are about to state formally.

Activity. Draw a segment $AB$ of length 6 cm. Plot a handful of points that are equidistant from $A$ and $B$ (you can do this with a compass by keeping the same radius from both $A$ and $B$). Join the points you plotted — you will find they all lie on one straight line, confirming that the perpendicular bisector really is a straight line.