Aim: How do we find the locus of points?

March 5,2012, Aim: How do we find the locus of points?

Answer:

Locus: The Locus is the set of all points that satisfy a given condition;  a general graph of a given equation.

*Their are five types of Locus of points:

*Locus of points equidistant from one point.
*Locus of points equidistant from two points.
*Locus of points equidistant from a single line.
*Locus of points equidistant from two parallel lines.
*Locus of points equidistant from two intersecting lines.


Locus of points equidistant from one point:
  The locus of points from a single point is a set of points, equidistant from the point in every direction. 


Example:

http://mathforum.org/mathtools/images/items/32615.gif

http://www.regentsprep.org/Regents/math/geometry/GL1/Adog.gif
The path in which the dog is moving is the locus of points 


Locus of points equidistant from two points:
   The locus of points equidistant from two points is the perpendicular bisector of the segment connecting the two points. 
Example:

http://kwiznet.com/px/homes/i/math/G9/Geometry/G9_Geometry_Locus_2.gif

http://www.mathwithlarry.com/lessons/locus3.jpg


Locus of points equidistant from a single line:
  The locus of points equidistant from a line are two lines, on opposite sides (equidistant and parallel lines on opposite sides of the original line.)
Example:

http://mathematics.nayland.school.nz/Year_11/AS1.8_Geometric_Repres/1.4_construction_images/images_locus/PicTh2.gif



Locus of points equidistant from two parallel lines:
  The locus of points equidistant from two lines is another line, half-way between both lines, and parallel to each of them.
Example:

http://www.regentsprep.org/Regents/math/geometry/GL1/PicTh4.gif

Locus of points equidistant from two intersecting lines:
  The locus of points equidistant from two intersecting lines are two additional lines that bisect the angles formed by the original lines that bisect the angles formed by the original lines( the two intersecting lines half-way between the original lines.)
Example:
http://www.regentsprep.org/Regents/math/geometry/GL1/PicTh5.gif

Try this Yourself:

What type of Locus theorem is expressed below?

Ben skis through a park that is bounded on two sides by straight intersecting streets.  Ben skis so that he is always the same distance from each street.  Describe Ben's path.

A) Locus of points equidistant from one point 

  B) Locus of points equidistant from two points.

     C) Locus of points equidistant from a single line.

              D) Locus of points equidistant from two parallel lines.

                      E) Locus of points equidistant from two intersecting lines.

Answer:
E) Locus of points equidistant from two intersecting lines.