A locus is a set of points which satisfies a certain condition.

theorem Locus Theorem 3
The locus equidistant from two points A and B, is the perpendicular bisector of the line segment joining the two points.

Does this theorem sound familiar? Remember our previous discussions of a perpendicular bisector?  
This theorem asks you to "describe the path formed by all points located the same distance from A as from B".
ANSWER: the perpendicular bisector of the segment from A to B.
Example 1: A tour guide informs visitors that at this time of day, the best photographs of this arena are taken from any location equidistant from the base of the two entry pillars, as shown. The tourists should stand on the line that is the perpendicular bisector of the segment joining the bases of the pillars.

Set of points: the tourists' locations
Condition: equidistant from pillars
Locus: a line which is the perpendicular bisector of the segment joining the two bases of the pillars

Example 2: Marlo's little brother is flinging mud balls with his slingshot. He pulls back on the slingshot, stretching the elastic pulls and releasing the mud ball so it travels in a straight line between the tops of the slingshot.

Set of points: the mud ball's locations
Condition: a straight projection
Locus: a straight line halfway between the two points and perpendicular to the segment joining the points


Example 3: The Hanover Castle's annual scavenger hunt is underway. After deciphering several sets of clues as to the location of a hidden key to a treasure, a group of friends have arrived at the Final Clue. Fortunately, the friends are avid mathematicians and can quickly find the line along which they need to search for the key.

Set of points: possible locations for key
Condition: equally distant from shrubs
Locus: a straight line halfway between the two shrubs and perpendicular to a segment joining the two shrubs



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