Solve problems involving loci

Loci in Two Dimensions

8.2

Loci in Two Dimensions

Locus of points that are of constant distance from a fixed point:

The locus of a point that is equidistant from a fixed point is a circle centered at that fixed point.
Points marked at the same distance from a fixed point \(O\) forms a circle.
A point that always moves at the same distance from a fixed point forms a circle.

Locus of points that are equidistant from two fixed points:

The locus of a point that is equidistant from two fixed points is the perpendicular bisector of the line connecting the two fixed points.
The two points of intersection are connected with a straight line.

Locus of points that are of constant distance from a straight line:

The locus of points that are of constant distance from a straight line is straight lines parallel to that straight line.

Locus of points that are equidistant from two parallel lines:

The locus of points that are equidistant from two parallel lines is a straight line parallel to and passes through the midpoints of the pair of parallel lines.

Locus of points that are equidistant from two intersecting lines:

The locus of points that are equidistant from two intersecting lines is the angle bisector of the angles formed by the intersecting lines.