Loci and Concurrency


   
 
Summary
 
  • A locus of points is the set of points, and only those points, that satisfy given conditions.
 
          - Every point satisfying the given conditions lies on the locus.
 
          - Every point on the locus satisfies the given conditions.
 
          - The locus can be a straight line or a curved line (lines).
 
  • To determine a locus:
 
          - State what is given and the condition to be satisfied.
 
          - Find several points satisfying the condition, which indicate the shape of the locus.
 
          - Connect the points and describe the locus fully.
 
  • The locus of points equidistant from the sides of a given angles is the bisector of the angle.
 
                   
 
  • The locus of points equidistant from two given intersecting lines is the bisectors of the angles formed by the lines.
 
               
 
  • The locus of points equidistant from two fixed points is the perpendicular bisector of the segment joining them.
 
                 
 
  • Locus of a point equidistant from a given point in a plane is a circle.
 
              
 
  • The locus of points equidistant from two given parallel lines is a line parallel to the two lines and midway between them.
 
           
 
  • Locus of all points at a given distance from a given line is two straight lines parallel to the given line.
 
 
                   
 
 
     
   
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