Name_________________________________
Geometry
Pd __________ Date________________
Teacher
1

Circles in the Coordinate Plane – Day 1 ……………………………………………………………………………………..…………….. Page 3
Locus – Day 2……………………………………. ………………………………………………………………………………………..…………….. Page 9
Locus in the Coordinate Plane – Day 3 ………………………………………………………………………..……………………….….….. Page 16
Compound Locus – Day 5………………………………….…………………………………………………………………..……..…………….. Page 22
Compound Locus in the Coordinate Plane – Day 6………………………………………………………………………..…………….. Page 29
Review of Locus ……………………………………………………………………………………………………………………………………………. Page 34
2

SWBAT: Write equations and graph circles in the coordinate plane.
Use the Distance Formula to find the distance, to the nearest tenth, between each pair of points.
2. C(4, 5) and D(0, 2) 1.
A(6, 2) and D(–3, –2)
Example 1A: Writing the Equation of a Circle
Model Problem:  J with center J (2, 2) and radius 4
Write the equation of each circle.
Practice #1
 L with center L (–5, –6) and radius 9
Practice #2
 P with center P(0, –3) and radius 8
3

Example 1B: Writing the Equation of a Circle
Model Problem: Writing the equation of  K that passes through J(6, 4) and has center K(1, –8).
Write the equation of each circle.
Practice #3
 Q that passes through (2, 3) and has center Q(2, –1)
Practice #4
 D that passes through (–2, –1) and has center D(2, –4)
4

Example 2: Graphing Circles
Model Problem:
Graph x 2 + y 2 = 16.
Practice #5
Graph x² + y² = 9.
Model Problem:
Graph (x – 3) 2 + (y + 4) 2
Practice #6
Graph (x – 3) 2 + (y + 2) 2 = 4.
= 9.
5

Homework
6

7

8

The plural of locus is loci.
When describing a locus, you must include two things:
1. The SHAPE of the locus. (Is it a circle? A line? Two lines?)
2. A DESCRIPTION of the locus.
A locus question may look like this:
To find the locus, we draw points that fit the condition and note the shape these points take on:
What SHAPE do the points form? ______________________________________
Let’s write a DESCRIPTION of the shape:

What is at the center of the circle? _________________________

What is the radius of the circle? ___________________________
9

What is the locus of points 2 inches from a given point?
: _______________________________________________________________
_______________________________________________________________________
A boy walks through a field that is bounded on two sides by straight, intersecting roads. He walks so that he is always equidistant from the two roads. Describe the shape of the possible paths he could take.
(What SHAPE does the locus take on? DESCRIBE the shape of the locus.)
Field
: _______________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
10

11

Here are the five most common given conditions for locus questions. Memorize them!
12

Sketch the locus of points equidistant from the two intersecting lines below.
13

Sketch the locus of points equidistant from the two parallel lines
Sketch the locus of points that are the given distance from line.
14

15

1.
Find the locus of points that are two units from the line whose equation is x = 3 and write the equation.
Practice
2.
Find an equation of a line that satisfies each of the following conditions: a.
All points 5 units from the line x = -3 b. All points 3 units from the line x - axis
16

3.
Find the locus of points equidistant from the points A (4, 5) and B (4, -1) and write the equation.
Practice
4.
Find the locus of points equidistant from the points below and write the equation. a.
A (2, 6) and B (2, -8) b. A (-3, -7) and B (0, -7)
17

1.
Find an equation of a line that describes the locus of points equidistant from the lines whose equations are y = 3x – 1 and y = 3x + 5.
Practice
Find an equation of a line that describes the locus of points equidistant from the equations below.
1.
Write an equation of the locus of points equidistant from the graphs of the equations x = 4 and x = -2.
2.
Write an equation of the locus of points equidistant from the graphs of the equations y = ½x – 4 and y = ½x + 2.
18

1.
Write an equation of the locus of points four units from the point (-2, 1).
Practice
Find an equation of a line that satisfies each of the following conditions: a.
5 units from the point (4, -2) b. 7 units from the origin.
19

Locus with Coordinate Geometry
Write an equation (or pair of equations) and draw the graph of the locus of all points
1) 3 units from the y-axis
2) 1 unit from the x-axis
3) 4 units from the y-axis
4) 5 units from the line y = 3
5) 3 units from the line x = -2
6) Equidistant from the two lines x = 1 and x = 5
7) Equidistant from the two lines y = 2 and y = -4
8) Equidistant from the x - axis and the line y = 6
9) Equidistant from the y - axis and the line x = -8
10) An equation of the locus of points that are at a distance of 8 units from the origin.
11) An equation of the locus of points that are 3 units from the point (1, -1).
12) Write an equation of the locus of points 4 units from the point (-2, 1)
20

21

22

Practice - Compound Locus
Note: All situations take place in a plane
1.
What is the number of points in a plane two units from a given line and three units from a given point on the line?
2.
Two points A and B are 4 units apart. How many points are there that are equidistant from both A and b and also 3 units from A?
3.
Parallel lines r and s are 8 meters apart, and A is a point on line s. How many points are equidistant from r and s and also 4 meters from A?
4.
A given point P is 10 units from a given line. How many points are 3 units from the line and 5 units from point P?
5.
Two points A and B are 7 units apart. How many points are there that are 12 units from A and also 4 inches from B?
23

24

Homework - Compound Locus
Note: All situations take place in a plane
1) Given point p on a line. The total number of points that are at a distance of 4 cm from P and also at a distance of 3 cm from the given line is
(a) 1 (b) 2 (c) 3 (d) 4
2) What is the total number of points that are 3 ft from a given line and 3½ ft from a given point on that line?
3) What is the total number of points that are 3 in from a given line and also 3 in from a given point on this line?
(a) 1 (b) 2 (c) 3 (d) 4
4) Given point P on line AB. What is the total number of points that are at a distance of 4cm from line AB and also at a distance of 10 cm from point P?
(a) 1 (b) 2 (c) 3 (d) 4
5) Given line m. What is the number of points at a fixed distance d from m and also equidistant from two points, A and B on m?
6) What is the total number of points that are equidistant from two intersecting lines m and n and also 3 in from line m?
7) The total number of points that are equidistant from two intersecting lines and also 5 inches from their point of intersection is:
(a) 1 (b) 2 (c) 3 (d) 4
8) Point P is 8 cm from line AB. How many points are 6 cm from point P and also 3 cm from line AB?
(a) 0 (b) 2 (c) 3 (d) 4
25

9) Points A and B are 5 in. apart. What is the total number of points that are 2 in. from A and also 4in. from B?
(a) 1 (b) 2 (c) 3 (d) 4
10) Parallel lines AB and CD are 6” apart and point P is on AB. The number of points that are equidistant from AB and CD and also 6” from P is:
(a) 1 (b) 2 (c) 0 (d) 4
11) Lines x and y are parallel and 4cm apart. Point P lies on line x. What is the locus of points 3 cm from P and also equally distant from lines x and y?
(a) one point (b) two points (c) one line (d) two lines
12) Points A and B are 4 in. apart. The number of points equidistant from both A and B and also 3 in. from A is:
(a) 1 (b) 2 (c) 3 (d) 0
13) What is the total number of points that are equidistant from the four vertices of a rectangle?
(a) 1 (b) 2 (c) 3 (d) 4
14) Point P is 2 inches from line CD. What is the total number of points that are 1 inch from line CD and also I inch from P?
(a) 1 (b) 2 (c) 3 (d) 4
15) Parallel lines l and m are 4 cm apart and P is a point on line l. The total number of points that are equidistant from l and m and also 2 cm from P is:
(a) 1 (b) 2 (c) 3 (d) 0
26

27

28

Compound Locus with Coordinate Geometry – Day 6
Example Problem
1) How many points are equidistant from (2,0) and (8,0) and also 5 units from the origin?
2) How many points are equidistant from y = 3 and y = 7 and also 7 units from (1, -2)?
3) How many points are 4 units from x = -3 and also 3 units from the origin?
29

4) How many points are 2 units from the y-axis and also 2 units from the origin?
5) Find the number of points that are 4 units from the origin and also 4 units from the x-axis.
6) Find the number of points that are equidistant from points P (2,1) and Q (2, 5) and are also 3 units from the origin.
30

7) ) Given the point A(3, 5) a) Describe fully the locus of points at a distance of d units from A. b) Describe fully the locus of points at a distance of one unit from the y – axis. c) How many points satisfy the conditions in both a and b if:
(1) d = 2 (2) d = 4 (3) d = 5
31

Homework – Compound Locus with Coordinate Geometry
1.
a) On graph paper, draw the locus of points 2 units from the line whose equation is
x = 1
b) Write the equation(s) of the locus described in a.
c) Describe fully the locus of points at a distance P from the point (2,3).
d) How many points satisfy the conditions in parts a and c simultaneously if:
P = 1 P=2 P=3
2.
a) Write an equation(s) of the locus of points 3 units from the y-axis. b) Describe fully the locus of points at a distance of d units from P (-1, 4) c) Find the number of points that simultaneously satisfy the conditions in parts a and b for the following values of d: d = 1 d = 2 d = 4
32

3) Given line x = -3 and line x = 5. a) Describe fully the locus of points equally distant from the two given lines. b) Write the equation(s) of the locus described in part a. c) Describe fully the locus of points d units from P (3,2). d) How many points simultaneously satisfy the conditions in parts a and c if d is: d = 1 d = 2 d = 5
4) Given the point P (-2,3) on the coordinate plane. a) Describe fully the locus of points at a distance d units from P. b) Describe fully the locus of points at a distance of two units from the x – axis. c) How many points simultaneously satisfy the conditions in parts a and b for the following values of d?
D = 1 d = 5 d = 6
33

34

35

36

37

38