Date___Geometry Honors Teacher

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Name______Pd ______Date______Geometry Honors Teacher

Table of Contents

Circles in the Coordinate Plane – Day 1 ……………………………………………………………………………………..…………….. Page 3

Locus – Day 2……………………………………. ………………………………………………………………………………………..…………….. Page 19

Locus in the Coordinate Plane – Day 3 ………………………………………………………………………..……………………….….….. Page 13

Compound Locus in the Coordinate Plane – Day 4………………………………………………………………………..…………….. Page 21

Compound Locus– Day 5…………………………………………………………..…………………………………………………..…………….. Page 26

Circles in the Coordinate Plane – Day 1

SWBAT: Write equations and graph circles in the coordinate plane. Warm Up

Use the Distance Formula to find the distance, to the nearest tenth, between each pair of points.

1. A(6, 2) and D(–3, –2) 2. C(4, 5) and D(0, 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 Practice #2

L with center L (–5, –6) and radius 9 P with center P(0, –3) and radius 8

Example 1B: Writing the Equation of a Circle

Model Problem: Writing the equation of K whose diameter has endpoints A(5, 4) and B(1, –8).

Write the equation of each circle.

Practice #3

Writing the equation of K whose diameter has endpoints A(2, 3) and B(2, –1).

Example 2: Graphing Circles

Model Problem: Model Problem:

Graph x2 + y2 = 16. Graph (x – 3)2 + (y + 4)2 = 9.

Practice #5 Practice #6

Graph x² + y² = 9. Graph (x – 3)2 + (y + 2)2 = 4.

Homework

Locus – Day 2

Practice

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

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

Exercise 4 Sketch the locus of points equidistant from the two parallel lines

Exercise 5 Sketch the locus of points that are the given distance from line.

Locus in the Coordinate Plane – Day 3

Model Problem #1: The locus of points a given distance from a line.

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: All points 5 units from the y-axis

Model Problem #2: The locus of points equidistant from two points.

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 (-3, -7) and B (0, -7)

5. Write the equation for the locus of points equidistant from points A(1, 4) and B(7,8).

Model Problem #3: The locus of points equidistant from two parallel lines.

6. 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 7. Write an equation of the locus of points equidistant from the graphs of the equations

y = ½x – 4 y = ½x + 2.

Model Problem #4: The locus of points a given distance from a point.

8. Write an equation of the locus of points four units from the point (-2, 1).

Practice

9. Find an equation of a line that satisfies each of the following conditions:

5 units from the point (4, -2)

Homework 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) 5 units from the line y = 3 4) Equidistant from (6, 5) and (-2, 5)

5) Equidistant from (2, -4) and (4, 8) 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)

13) Write an equation of the locus of points equidistant from the graphs of the equations: y = 4x – 4 y = 4x + 4.

14) Write an equation of the locus of points equidistant from the graphs of the equations: y = ⅞x – 10 y = ⅞x + 8.

15) Write an equation of the locus of points equidistant from the graphs of the equations: y = ⅔x + 6 y = ⅔x + 2 18

Compound Locus with Coordinate Geometry – Day 4

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?

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.

Homework – Compound Locus with Coordinate Geometry

1. Find the locus of points that are 4 units from the origin and equidistant from the points S (1,0) and T(3,0).

2. Find the locus of points that are 1 unit from the x-axis and 3 units from the origin.

3. Determine the number of points that are equidistant from the x- and y-axes and 5 units from the origin.

4. Determine the number of points that are equidistant from (4,2) and (-2,2) and 3 units from the point (3,-2).

5. Determine the number of points that are 1 unit from the x-axis and 2 units from the point (5,3).

6. Graph the locus of points that are 4 units from the x-axis and 1 unit from the y-axis.

7. Solve the following: a. Draw the locus of points 3 units from the y-axis and write the equation for this locus. b. Draw the locus of points 4 units from the origin and write the equation for this locus. c. How many points that satisfy both conditions stated in parts a and b?

8. Solve the following: a. Draw the locus of points equidistant from the points (4,1) and (4,5) and write the equation for this locus.

b. Draw the locus of points equidistant from the points (3,2) and (-4,2).

c. Find the number of points that satisfy both conditions stated in a and b.

Compound Locus with Coordinate Geometry – Day 5

Example 1: A treasure is buried in your backyard. The picture below shows your backyard which contains a stump, a teepee, and a tree. The teepee is 8 feet from the stump and 18 feet from the tree. The treasure is equidistant from the teepee and the tree AND ALSO 6 feet from the stump. Locate all possible points of the buried treasure.

Example 2: Two points A and B are 6 units apart. How many points are there that are equidistant from both A and B and also 5 units from A?

Example 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?

Example 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?

Example 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?

Homework