What is a locus?

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Perpendiculars, Bisectors and Locus 4-3C

• What is a locus?
• What is the relationship between a perpendicular
  bisector of a segment and the segments
  endpoints?
• What is the relationship between the points on an
  angle bisector and the angle sides?

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Definition
A locus is the set of all the points that satisfy
a given condition.
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Determine the locus of points in a plane 1 in.
from a given point Q.
What do you get?
Q
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Try It
Describe the locus of points in space that are 2
in. from a given point C.
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Build it there
You will need a piece of paper, a rule, and a
protractor. Turn to page 300 in your book.
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Perpendicular Bisector
A perpendicular bisector of a segment is a line,
ray, segment or plane this is perpendicular to
the segment and divides it into two congruent
segments.
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Theorem
A point is on the perpendicular bisector of a
segment if and only if it is equidistant from the
endpoints of the segment.
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Theorem
A point is on the angle bisector of an angle if
and only if it is equidistant from the sides of
the angle.
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What is a locus? A locus is the set of all the
points that satisfy a given condition. What is
the relationship between a perpendicular bisector
of a segment and the segments endpoints? The
points on the perpendicular bisector of a segment
are equidistant from the segments
endpoints. What is the relationship between the
points on an angle bisector and the angle
sides? The points on an angle bisector are
equidistant from the angle sides.
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Assignment 4-3C
Page 301, 1-4, 7, 8, 12