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

> The Locus is the set of all points that satisfy a given condition.

--There are different ways the locus of points can come out to be like:

1. The locus of points equidistant from a single point is a set of points equidistant from the point in every direction. 

*Example:

The locus of points at a fixed distance, d, from point P is a circle with the given point P as its center and d as its radius.

Hint: It comes out to be a circle with the original point at its center!

2. The locus of points equidistant from 2 points is the perpendicular bisector of the line segment determined with the 2 points.

*Example:

The locus of points equidistant from two points, P and Q, is the perpendicular bisector of the line segment determined by the two points.
 

EASY HUH ? :)

 3. The locus points equidistant from a line are 2 lines on opposite sides equidistant and parallel to that line.

* Example:

The locus of points equidistant from two parallel lines, l₁ and l₂ , is a line parallel to both l₁ and  l₂ and midway between them.

 

3. The locus of points equidistant from two intersecting lines are two additional lines that bisect the angles formed by the original lines (two intersecting lines half way between the two original lines.)

*Example: 

  The locus of points equidistant from two intersecting lines, l₁ and l₂, is a pair of bisectors that bisect the angles formed by l₁ and l₂ .

ALWAYS REMEMBER : 

Remember:
A locus is just a set of points.

NOW YOU GIVE IT A TRY !!!

1.  Point A and point B are 26 miles apart. How many points are 20 miles from point A and 22 miles from point B?     

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* WRITE ANSWER BELOW IN COMMENTS* 

*Pictures and animation from regentsprep.org*