Name:___________________________________
Locus: Notes Packet
Date:______ Period:_____
Ms. Anderle
Locus: Notes Packet
A ________________________ is a set of all points that satisfy a given condition.
Think of locus as a “bunch” of points that all do the same thing. The plural of locus is
loci. Locus must always be drawn as a _____________________.
5 Basic Loci:
 Locus of a Point: _____________________________________________________
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___________________________________________________________________
Diagram:

Points Equidistant from Two Points:_______________________________________
___________________________________________________________________
___________________________________________________________________
Diagram:

Locus a Fixed Distance from a Line: ______________________________________
___________________________________________________________________
___________________________________________________________________
Diagram:

Equidistant from Two Parallel Lines:______________________________________
___________________________________________________________________
___________________________________________________________________
Diagram:

Equidistant from Intersecting Lines: ______________________________________
___________________________________________________________________
___________________________________________________________________
Diagram:
Locus a Fixed Distance from a Point:
Remember: The locus a fixed distance from a point is a _______________________.
When we draw the locus a fixed distance from a point on the coordinate plane, we must
use the equation of a _____________________.
Recall The Equation:
Examples:
1) Draw the locus of points that are 2 inches away from point J.
2) When he is not attached to the house, Fido is tied to a stake in the backyard. His
leash, attached to the stake, is 15 feet long. When traveling at the end of his
leash, what is the locus of Fido’s path? Draw the locus.
3) What is the locus of points that is 3 inches from point K.
4) Draw and state the equation of the locus 3 units away from point (-2,3).
5) Graph and state the locus 6 units away from point (-1, -3).
6) Graph and write the equation of the locus 5 units away from point (0, 2).
7) Graph and state the equation of the locus 3 units away from (1, -3).
Locus Equidistant from Two Points:
Recall: The locus equidistant from two points is the _____________________________
of the line segment that connects those two points.
Since the locus of points equidistant from two points is the perpendicular bisector, we
must write the equation of the line perpendicular to the segment connecting those two
points that goes through the midpoint of the segment.
Therefore, we must find the midpoint of the segment connecting the two given points,
as well as the slope of the segment connecting the two given points.
Recall: Perpendicular lines have _________________________________.
Slope Formula:
Midpoint Formula:
Equation of a line using Point-Slope Formula:
Examples:
1) You are playing a game of paint ball. Two of your friends are hiding behind trees
that are 10-feet apart. Where could you possibly stand so that your firing distance
to each friend is exactly the same?
2) There are two buoys in a lake. A scuba diver swims so that he is always
equidistant from both buoys. Describe his path.
3) Two houses are 180 feet apart. The underground electrical cable used to service
the house is to be placed such that the distance from any point on the cable is to
each home is always the same distance. Draw a picture and describe where the
cable should be placed.
4) What is the equation of the locus of points equidistant from the points (4,2) and
(-2,2)? Graph the locus.
5) What is the equation of the locus of points equidistant from (4,-2) and (4,4)?
Graph.
6) What is the equation of the locus of points equidistant from the points (3,5) and
(-1,3). Graph the points and the locus.
7) What is the equation of the locus of points equidistant from (-2,1) and (6.5).
Graph the two points and the locus.
Locus a Fixed Distance from a Line:
Recall: The locus a fixed distance from a line is ________________________________
Examples:
1) Sketch the locus of points 5 miles away from line T.
2) 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. If you and all of your classmates
stand exactly 3 feet away from the line, describe where you and your classmates
will be standing.
3) A straight driveway is 25 feet long and 8 feet wide. A gardener is planning to
plant flowers 6 feet from the center of the driveway. Describe where the flowers
will be planted. Draw a picture.
4) Graph and write the equation of the locus of points 5 units away from the line
x=2.
5) Graph and write the equation of the locus of points 4 units away from the line
y= -1.
Locus Equidistant from Two Parallel Lines:
Recall: The locus equidistant from two parallel lines is the parallel line midway between
them.
Examples:
1) Sketch the locus of points equidistant from lines J and A.
2) During your morning jog, you run down an alley between two buildings which are
parallel to one another and are 20 feet apart. Describe your path through the
alley so that you are always the same distance from each building. Sketch a
picture to represent the locus.
3) Graph and write the equation of the locus equidistant from the lines x = -2 and
x = 6.
4) Graph and write the equation of locus equidistant from the lines y = 3 and y = 7.
5) Write the equation of the locus of points equidistant from the lines y= -2 and y=5.
Locus of Points Equidistant from Two Intersecting Lines:
Recall: The locus of points equidistant from two intersecting lines is the bisectors of
each pair of vertical angles formed by the lines.
Examples:
1) Sketch the locus of points in the diagram below.
2) Sketch the locus of points equidistant from the x- and y-axis.