When a point moves in a plane according to some given conditions the path along which it moves is called a locus.
Locus Theorem
Locus Theorem 1: The locus of points at a fixed distance,
d, from the point,
P is a circle with the given point
P as its center and d as its radius.
Locus Theorem 2: The locus of the points at a fixed distance,
d, from a line,
I, is a pair of parallel lines
d distance from
I and on either side of
I.
Locus Theorem 3: The locus of points equidistant from two points, P and Q , is the perpendicular bisector of the line segment determined by the two points.
Locus Theorem 4: The locus of points equidistant from two parallel lines, I1 and I2, is a line parallel to both I1 and I 2 and midway between them.
Locus Theorem 5: The locus of points equidistant from two intersecting lines, I1 and I2, is a pair of bisectors that bisect the angles formed by I1 and I2.