10.7 Locus

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10.7 Locus

• p. 642

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Locus

• Definition the set of all points in a plane
  that satisfy a given condition or a set of given
  conditions.
• Plural Loci
• Pronounced low-sigh

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Ex what is the locus of points that the end of
the second hand on a clock forms?

• A circle

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Ex Draw a line k on a piece of paper. Draw
describe the locus of points on the paper that
are 1 cm from the line k.
k
1 cm
m
1 cm
2 lines, m n, ?? to line k and 1 cm away on
either side.
n
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4 steps to finding a locus

• Draw any figures that are given.
• Locate several pts that satisfy the condition.
• Continue until a pattern is recognized.
• Draw the locus describe it in words.

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Finding locus for 2 or more conditions

• Find the locus for each individual condition 1st.
• Then, find the intersection of the conditions.
• This intersection is the solution.

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Ex Given ?ABC, what is the locus of points that
are dist from AB AC and also dist from A B?
? bisector of ?A
A
Intersection of the 2 lines is the solution.
B
? bisector of AB
C
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Ex What is the locus of pts 2 cm from X 3 cm
from Y?
If XY gt 5, locus is 0 pts.
2
3
If XY 5, locus is 1 pt.
X
Y
If XY lt 5, locus is 2 pts.
X
2
3
Y
3
Y
2
X
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Definitions

• Epicenter the pt. on the surface of the earth
  directly above an earthquakes origin.
• Seismograph tool that measures distance to the
  epicenter, but not the direction to the
  epicenter.
• To locate an epicenter, 3 locations for
  seismographs are needed.
• The place where all 3 circles intersect is the
  epicenter.

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Ex 3 readings from seismographs are as follows
at A(2,4) epicenter is 2 miles away, at
B(2,-.5) epicenter is 2.5 miles away, at
C(-1,2) epicenter is 3 miles away. Where is
the epicenter?
A
C
(2,2)
B
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Assignment