Locus: Equidistant from Two
Parallel Lines

Topical Outline | Geometry Outline | MathBits' Teacher Resources

Terms of Use   Contact Person: Donna Roberts

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

theorem Locus Theorem 4
The locus equidistant from two parallel lines m1 and m2 , is a line parallel to both m1 and m2 and halfway between them.

This theorem asks you to "describe the path formed by all points the same distance from two parallel lines".
ANSWER: one line halfway between the parallel lines. All three lines are parallel.
Example 1: When luge athletes are learning how to control their sleds, they practice in straight line runs with the goal of keeping the sled in the middle of the run, at equal distances from both side walls.

Set of points: the sleds' locations
Condition: equidistant from side walls
Locus: one line parallel to the side walls and halfway between the walls.

Example 2: During her morning run, Camilla jogs down an alley between two buildings that are parallel to one another and are 6 feet apart. Since Camilla likes to maintain an equal distance from each building, she jogs on a straight line parallel to the buildings and halfway between them. She jogs 3 feet from each building.

Set of points: Camilla's location
Condition: equidistant from buildings
Locus: a straight line halfway between the two buildings and parallel to both buildings



NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation
and is not considered "fair use" for educators. Please read the "Terms of Use".