The document defines 'locus' as the set of points that satisfy certain conditions in a plane. It outlines the steps for finding a locus based on one or more conditions and provides examples to illustrate these concepts. Additionally, it includes definitions related to epicenters and seismographs, explaining how to determine the location of an epicenter using distance measurements from multiple points.

1. 10.7 Locus10.7 Locus
p. 642p. 642

2. LocusLocus
Definition: the set of all points in aDefinition: the set of all points in a
plane that satisfy a given conditionplane that satisfy a given condition
or a set of given conditions.or a set of given conditions.
Plural – LociPlural – Loci
Pronounced: “low-sigh”Pronounced: “low-sigh”

3. Ex: what is the locus of pointsEx: what is the locus of points
that the end of the second handthat the end of the second hand
on a clock forms?on a clock forms?
A circleA circle

4. ExEx: Draw a line k on a piece of: Draw a line k on a piece of
paper. Draw & describe the locus ofpaper. Draw & describe the locus of
points on the paper that are 1 cmpoints on the paper that are 1 cm
from the line k.from the line k.
kk
1 cm1 cm
1 cm1 cm
mm
nn
2 lines, m & n,2 lines, m & n,  toto
line k and 1 cm awayline k and 1 cm away
on either side.on either side.

5. 4 steps to finding a locus4 steps to finding a locus
1.1. Draw any figures that are given.Draw any figures that are given.
2.2. Locate several pts that satisfy theLocate several pts that satisfy the
condition.condition.
3.3. Continue until a pattern isContinue until a pattern is
recognized.recognized.
4.4. Draw the locus & describe it inDraw the locus & describe it in
words.words.

6. Finding locus for 2 or more conditionsFinding locus for 2 or more conditions
Find the locus for each individualFind the locus for each individual
condition 1condition 1stst
..
Then, find the intersection of theThen, find the intersection of the
conditions.conditions.
This intersection is the solution.This intersection is the solution.

7. Ex: GivenEx: Given ΔΔABC, what is the locusABC, what is the locus
of points that areof points that are =dist from AB &=dist from AB &
ACAC and alsoand also =dist from A & B=dist from A & B??
AA
BB
CC
Intersection of the 2Intersection of the 2
lines is the solution.lines is the solution.
∠∠ bisector ofbisector of ∠∠AA
⊥⊥ bisector of ABbisector of AB

8. ExEx: What is the locus of pts 2 cm: What is the locus of pts 2 cm
from X & 3 cm from Y?from X & 3 cm from Y?
22 33
XX YY
If XY > 5, locus is 0 pts.If XY > 5, locus is 0 pts.
22
22
33
33
If XY = 5, locus is 1 pt.If XY = 5, locus is 1 pt.
XX
XX
YY
YY
If XY < 5, locus is 2 pts.If XY < 5, locus is 2 pts.

9. DefinitionsDefinitions
Epicenter – the pt. on the surface of the earthEpicenter – the pt. on the surface of the earth
directly above an earthquake’s origin.directly above an earthquake’s origin.
Seismograph – tool that measures distance toSeismograph – tool that measures distance to
the epicenter, but not the direction to thethe epicenter, but not the direction to the
epicenter.epicenter.
To locate an epicenter, 3 locations forTo locate an epicenter, 3 locations for
seismographs are needed.seismographs are needed.
The place where all 3 circles intersect is theThe place where all 3 circles intersect is the
epicenter.epicenter.

10. ExEx: 3 readings from seismographs are as: 3 readings from seismographs are as
follows: at A(2,4) – epicenter is 2 miles away,follows: at A(2,4) – epicenter is 2 miles away,
at B(2,-.5) – epicenter is 2.5 miles away, & atat B(2,-.5) – epicenter is 2.5 miles away, & at
C(-1,2) – epicenter is 3 miles away. Where isC(-1,2) – epicenter is 3 miles away. Where is
the epicenter?the epicenter?
AA
BB
CC
(2,2)(2,2)

11. AssignmentAssignment