Locus
Page 2 & 4
Sketch the five fundamental loci in your notes please.
1. Given: A and B
4. Given: AB CD
Find points equidistant from
these two fixed points
Find points equidistant from
these two parallel lines
2. Given: AB intersecting CD
Find points equidistant from
these two intersecting lines
5. Given : Point A and distance d .
Find points that are at a distance
d from the fixed point A.
d
3. Given: AB and a distanced.
A
Find points that are at a
distance
d from the line
A
d
B
C
1
4
A
B
A
B
C
D
2
D
C
5
A
B
d
A
D
3
d
A
d
B
Essential Question:
What are the five
fundamental Locus?
Recall our procedure from yesterday:
1) Make a diagram of the fixed points or lines
2) Locate a point that satisfies the condition.
Then locate several other points that satisfy it.
3) Through the points, draw a dotted line or
smooth curve of the locus.
4) Describe in words the locus.
Page 2
3. What is the locus of a car that is being driven down a street
equidistant from the two opposite parallel curbs.
The locus of points
is a third line,
parallel to the curbs,
midway between
them.
4. A dog is tied to a stake by a rope 6 meters long. Discover the
boundary of the surface over which he may roam.
6m
The locus of points is a circle
centered at the stake, with a
radius of 6 m.
Now try 5-12
on page 2 of
your packet.
Page 2
The locus of points is the angle
bisector of the angle formed by
the two intersecting roads.
The locus of points is the
perpendicular bisector of the
segment formed between the
two floats.
Page 2
10 cm
The locus of points is a circle
centered at the given point, with
a radius of 10 cm.
B
The locus of points is the
perpendicular bisector of the
segment joining A and B
A
We are now going to look
at how locus can be used
in the coordinate plane.
17. Write an equation of the locus of all points:
a. 2 units from the x-axis and above it. y  2
b. 5 units from the y-axis and to the right of it. x  5
c. 4 units from the y-axis and to the left of it. x  4
d. 3 units from the x-axis and below it. y  3
e. Equidistant from the x-axis and the y-axis y  x
and whose coordinates are the same.
Remember HOY - VUX:
H - ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑙𝑖𝑛𝑒
O - 𝑧𝑒𝑟𝑜 𝑠𝑙𝑜𝑝𝑒
Y-𝑦=#
V - 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑙𝑖𝑛𝑒
U - 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑠𝑙𝑜𝑝𝑒
X-𝑥=#
Page 4
18. Write the equation of the line passing through the point 3,4
and perpendicular to the x-axis. x  3
20. Write an equation of the line passing through the point 5,2
and perpendicular to the y-axis. y  2
Page 4
22. Determine whether the point 8, −2 is on the locus whose
equation is given:
a. 𝑥 + 𝑦 = 6
b. 𝑦 = 10 − 𝑥
a) x  y  6
8  (2)  6
66
b) y 10  x
 2  10  8
2 2
yes
No
c. 𝑥 = 8
c) x  8
88
yes
Page 4
Page 4
24. A point is on the locus whose equation is 𝑥 − 𝑦 = 3. If the ordinate
of the point is 2, its abscissa is: (1) 1 (2) -1 (3) 5 (4) -5
25. A point is on the locus whose equation is 3𝑥 − 𝑦 = 12. If the
abscissa of the point is 3, its ordinate is: (1) 5 (2) -3 (3) 3 (4) 4
26. An equation that represents the locus of all points 9 units to the left
of the y-axis is: (1) 𝑥 = 9 (2) 𝑥 = −9 (3) y = 9 (4) y = −9
24) x  y  3
x23
2 2
x5
25) 3x  y  3
3(3)  y  12
9 - y  12
9 9
 y3
y  3
Essential Question:
What are the five
fundamental Locus?
Homework
Page 2
13,14,15
Page 4
19, 21, 22 d,e,f
Page 2
The locus of points is one
line, parallel to the
horizontal line.
The locus of points is a circle
whose center is the center of the
steering wheel, with a radius the
radius of the steering wheel.
Page 2
4m
4m
4”
4”
The locus of points is a line
parallel to the original lines
midway between them.
The locus of points is 2 lines parallel
to the original line on each side 4”
away from the original.
Page 2
3
3
The locus of points is a line
parallel to the original lines
midway between them.
The locus of points is a line parallel
to the opposite sides of the square,
midway between them.
Page 2
The locus of points is the
perpendicular bisector of the
segment joining A and B
16. What is the locus of the center of a penny that is rolling around a quarter if the
edges of the two coins are always touching each other.
25¢
1¢
The locus of points is a circle
with a radius that extends from
the center of the quarter to the
center of the penny.
Page 4
x  1
y  4
Page 4
d ) x  y  10
8  (2)  10
10  10
yes
1
e) y  x
4
1
 2  (8)
4
2 2
No
f ) x  4y  0
8  4(2)  0
8  (8)  0
00
yes