Consider:
Your teacher has placed a strip of tape on the classroom floor which forms
a straight line. The teacher gives each student a yard stick and
asks that each student stand exactly 3 feet away from the line on the
floor.
Can you picture what will happen? If you, and all of your
classmates, stand exactly 3 feet away from the line, describe where you
and your classmates will be standing.
Answer:
You and your classmates will form two straight lines on either side of the tape on the floor,
at a distance of 3 feet away from the tape.
You
and your classmates are the locus of points equally distant (equidistant) from a given line (the tape on the floor).
Stated formally, we have our next locus theorem.
| Locus
Theorem 2: (line) |
|
The locus of
points at a fixed distance, d,
from a line, l,
is a pair of parallel lines d
distance from l
and on either side of l.
|
